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5^s I 



ELEMENTARY LESSONS 



IN 



ELECTRICITY and MAGNETISM 



A MAP OF ENGLAND, 

SHEWING THE LINES OF EQUAL MAGNETIC DECLINATION 
AND THOSE OF EQUAL DIP A INTENSITY. 

FOR THE YEAR. 1888 




Sbtn/br/ta Ceoy * if jtti^' 



ELEMENTARY LESSONS 

IN 

Electricity and Magnetism 



SILVANUS P. THOMPSON, D.Sc, B. A., F. R. A. S. 

Principal of and Professor of Physics in the City and 

Guilds of London Technical College, Finsbury ; 

Late Professor of Experimental Physics 

in University College, Bristol. 



REVISKD AND KNI.ARGED TO DATE, INCI.UDING AI,!, OF THE 

RECENT DISCOVERIES IN X-RAYS, WIREI.ESS 

TEI.EGRAPHY, ETC. 

BY PROF. OTTO H. I^. SCHWETZKY, 

I.EIPSIC, GERMANY. 



Thompson & Thomas 

CHICAGO 

1906 



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GK<4 



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QC- 



LIBRARY df CONGRESS 

Two CoDies Received 

2 1906 



(P Coay right Entry 

CLASS '^' 
t3 



nt Entry . 
, XXp. No, 



COPY B, 



Copyright 1906, by 
Thompson & Thomas 



PREFACE. 

These Lessons in Electricity and Magnetism are in- 
tended to afford to beginners a clear and accurate knowl- 
edge of the experiments upon which the Sciences of Elec- 
tricity and Magnetism are based, and of the exact laws 
which have been thereby discovered. The difficulties 
which beginners find in studying many modern text-books 
arise partly from the very wide range of the subject, and 
partly from want of familiarity with the simple fundamental 
experiments. We have, at the outset, three distinct sets 
of phenomena to observe, viz. — those of Frictional Electri- 
city, of Current Electricity, and of Magnetism ; and yet it 
is impossible to study any one of these rightly without 
knowing something of them all. Accordingly, the first 
three chapters of this work are devoted to a simple expo- 
sition of the prominent experimental facts of these three 
branches of the subject, reserving until the later chapters 
the points of connection between them, and such parts of 
electrical theory as are admissible in a strictly elementary 
work. No knowledge of algebra beyond simple equations, 
or of geometry beyond the first book of Euclid, is assumed. 

A series of Exercises and Problems has been added at 
the end of the book in order that students, who so desire, 
may test their power of applying thought to what they 
read, and of ascertaining, by answering the questions or 
working the problems, how far they have digested what 
they have read and made it their own. 

Wherever it has been necessary to state electrical 



vi PREFACE. 

quantities numerically, the practical system of electrical 
units (employing the volt^ the ohm^ and the ampere^ as units 
of electromotive-force, resistance and current, respectively) 
has been resorted to in preference to any other system. 
The author has adopted this course purposely, because he 
has found by experience that these units gradually acquire, 
in the minds of students of electricity, a concreteness and 
reality not possessed by any mere abstract units, and be- 
cause it is hoped that the lessons will be thereby rendered 
more useful to young telegraphists to whom these units are 
already familiar, and who may desire to learn something 
of the Science of Electricity beyond the narrow limits of 
their own practical work. 

Students should remember that this little work is but 
the introduction to a very widely- extended science, and 
those who desire not to stop short at the first step should 
consult the larger treatises of Faraday, Maxwell, Thom- 
son, Wiedemann, and Mascart, as well as the more 
special works which deal with the various technical 
Applications of the Science of Electricity to the Arts 
and Manufactures. Though the Author does not think 
it well in an elementary text-book to emphasize particular 
theories on the nature of Electricity upon which the 
highest authorities are not yet agreed, he believes that 
it will add to a clear understanding of the matter if he 
states his own views on the subject. 

The theory of electricity adopted throughout these 
Lessons is, that Electricity, whatever its true nature, is 
one, not two: that this Electricity, whatever it may 
prove to be, is not matter, and is not energy ; that it 



PREFACE. vli 

resembles both matter and energy in one respect, how- 
ever, in that it oan neither be created nor destroyed. 
The doctrine of the Conservation of Matter^ established 
a century ago by Lavoisier, teaches us that we can 
neither destroy nor create matter, though we can alter 
its distribution, and its forms and combinations, in 
innumerable ways. The doctrine of the Conservation 
of Energy^ which has been built up during the past 
half-century by Helmholtz, Thomson, Joule, and Mayer, 
teaches us that we can neither create nor destroy energy, 
though we may change it from one form to another, 
causing it to appear as the energy of moving bodies, or 
as the energy of heat, or as the static energy of a body 
which has been lifted against gravity, or some other 
attracting force, into a position whence it can run down, 
and where it has the potentiality of doing work. So 
also the doctrine of the Conservation of Electricity^ now 
growing into shape,^ but here first enunciated under 
this name, teaches us that we can neither create nor 
destroy Electricity though we may alter its distribution, 
— may cause more to appear at one place and less at 
another, — may change it from the condition of rest to 
that of motion, or may cause it to spin round in whirl- 
pools or vortices, which themselves can attract or repel 
other vortices. According to this view all our electrical 
machines and batteries are merely instruments for alter- 
ing the distribution of Electricity by moving some of it 

I This is undoubtedly the outcome of the ideas of Maxwell and of Faraday 
as to the nature of Electricity. Since the above was written an elegant 
analytical statement of the "Doctrine of the Conservation of Electricity" has 
been published by Mons. G. Lippmann, who had independently, and at an 
earlier date, arrived at the same view. 



Vlll PREFACE. 

from one place to another, or for causing Electricity, 
when accumulated or heaped together in one place, to 
do work in returning to its former level distribution. 
Throughout these lessons the attempt has been made 
to state the facts of the Science in language consonant 
with this view, but at the same time rather to lead the 
student to this as the result of his study than to insist 
upon it dogmatically at the outset. 



City and Guilds Technical College, 

FiNSBURY, November, 1905. 

PREFACE 
TO ONE HUNDREDTH THOUSAND. 

The ideas of Faraday, as enlarged and developed by 
Clark Maxwell, which were just beginning to be under- 
stood in 1888, by a few advanced minds, have conquered 
the whole world of science, although even to-day their 
full logical consequences are appreciated by few. It 
is still to many incomprehensible that the conducting 
wire does not carry the electric energy, but serves only 
as a guide. 

Besides the changes and additions necessitated by 
these great strides made by physicists and inventors, 
the startling discoveries of Marconi, Roentgen and 
others have also been carefully embodied in the pres- 
ent edition of this volume. 

Otto H. L. Schwetzky. 



CONTENTS, 

Part First. 

CHAPTER L 
Frictional Electricity, 

LESSON PAGE 

I. Electrical Attraction and Repulsion . . . i 
II. Electroscopes u 

III. Electrification by Induction . . . .18 

IV. Conduction and Distribution of Electricity . 28 
V. Electrical Machines .40 

VI. The Leyden Jar and other Accumulators . . 53 
VII. Other Sources of Electricity 62 

CHAPTER II. 

Magnetism. 



VIII. Magnetic Attraction and Repulsion 

IX. Methods of Making Magnets 

X Distribution cf Magnetism 

XI. Laws of Magnetic Force 

Note on Ways of Reckoning- Angles and Solid-Angles 
Table of Natural Sines and Tangents , 

XII. Terrestrial Magnetism . 



72 
82 
87 

95 
108 
III 

1X2 



CONTENTS. 



CHAPTER III. 



Current Electricity. 

LESSON PAGJ 

XIII. Simple Voltaic Cells .... 122 

XIV. Chemical Actions in the Cell . . • 131 
XV. Voltaic Batteries 137 

XVI. Magnetic Actions of the Current . . 150 

XVII. Galvanometers 161 

XVIII. Chemical Actions of the Current. Voltameters 171 
XIX. Physical and Physiological Effects of the 

Current . . . . • • i^o 



Part Second. 

CHAPTER IV. 
Electrostatics. 

XX. Theory of Potential 

Note on Fundamental and Derived Units 

XXI. Electrometers . . 

XXII. Specific Inductive Capacity, etc. 

XXIII. Phenomena of Discharge 

XXIV. Atmospheric Electricity . . 



190 
208 
211 
220 

23s 
253 



CHAPTER V. 
Electromagnetics. 

XXV. Theory of Magnetic Potential 

Note on Magnetic and Electromagnetic Units 
Note on Measurement of Earth's Magnetic Force in 

Absolute Units . • 

Note on Index Notation • 

XXVI. Electromagnets . . 
XXVII. Electrodynamics 
XXVIII. Diamagnetism 



265 
281 

284 
285 
286 
298 
306// 



CONTENTS. XI 



CHAPTER VI. 

Measurement of Currents, etc. 

LESSON PAGE 

XXIX. Ohm*s Law and its Consequences . . . 307 
XXX. Electrical Measurements 316 

CHAPTER VH. 
Heat, Light, and Work, from Electric Currents. 

XXXI. Heating Effects of Currents 328 

XXXII. The Electric Light 333 

XXXIII. Electromotors (Electromagnetic Engines) . . 340 

CHAPTER VHI. 

Thermo-Electricity. 
XXXIV. Thermo-Electric Currents 346 

CHAPTER IX. 

Electro-Optics. 

XXXV. General Relations between Light and Electricity 353 

CHAPTER X. 

Induction Currents (Magneto-Electricity). 

XXXVI. Currents produced by Induction .... 361 
XXXVII. Magneto-electric and Dynamo Electric Gen- 
erators . 375 

CHAPTER XI. 

Electro-Chemistry. 
XXXVIIL Electrolysis and Electrometallurgy . . . 387 



XU CONTENTS. 

CHAPTER XII. 
Telegraphs and Telephones. 

LESSON PAGE 

XXXIX. Electric Telegraphs 401 

XL. Electric Bells, Clocks, and Telephones . , 411 

CHAPTER XIII. 

Wireless Telegraphy. 

XLL Ether Waves 421 

XLII. Wireless Telegraph Apparatus .... 424 

CHAPTER XIV. 

X-Rays. 

XLIII. Vacuum and Cathode Rays ..... 430 
XLIV. X-Rays . 435 

CHAPTER XV. 

XLV. The Central Station 446 

XLVI. Modern Dynamos and Motors . . . .451 

APPENDIX. 

Problems and Exercises 463 

Index to Chapters I-XII 481 

Index to Chapters XIII-XV 49^ 



ELEMENTARY LESSONS 

ON 

ELECTRICITY & MAGNETISM. 
i9act ^it0U 



CHAPTER I, 

FRICTIONAL ELECTRICITY. . 

Lesson I. — Electrical Attrcu:iion and Repulsion. 

1. Electrical Attraotioru — If you take a piece of 
sealing-wax, or of resin, or a glass rod, and rub it upon 
a piece of flannel or silk, it will be found to have ac- 
quired a property which it did not previously possess : 
namely, the power of attracting to itself such light 
bodies as chaff, or duit, or bits of paper (Fig. i). This 
curious power was originally discovered to be a property 
of amber, or, as the Greeks called it, T^Xe/crpov, which 
is mentioned by Thales of Miletus (B.C. 600), and by 
Theophrastus in his treatise on Gems, as attracting light 
bodies when rubbed. Although an enormous number of 
substances possess this property, amber and jet were the 
only two in which its existence had been recognised by 
the ancients, or even down to so late a date as the time 
of Queen Elizabeth. About the year 1600, Dr. Gilbert 
of Colchester discovered by experiment that not only 

i& B 



^ ELEMENTARY LESSONS ON [chap. i. 

amber and jet, but a very large number of substances, 
such as diamond, sapphire, rock-crystal, glass, sulphur, 
sealing-wax, resin, etc., which he styled electrics^ 
possess the same property. Ever since his time the 
name electricity has been employed to denote the 
agency at work in producing these phenomena. Gilbert 
also remarked that these experiments are spoiled by tho 
presence of moisture. 



^fe^ 




Fig. I. 

2. A better way of observing the attracting force is 
to employ a small ball of elder pith, or of cork, hung by 
a fine thread from a support, as shown in Fig. 2. A 
dry warm glass tube, excited by rubbing it briskly with 
a silk handkerchief, will attract the pith ball strongly, 
showing that it is highly electrified. The most suitable 
rubber, if a stick of sealing-wax is used, will be found to 

1 ^* Eiectrica ; quae attrahunt eadem ratione ut electrum." — (GHbert). 



CHAP. I.] ELECTRICITY AND MAGNETISM. 



be flannel, woollen cloth, or, best of all, fur 
discovered that an electri- 
fied body is itself at- 
tracted by one that has 
not been electrified. This 
may be verified (see Fig. 
3) by rubbing a stick of 
sealing-wax, or a glass rod, 
and hanging it in a wire 
loop at the end of a silk 
thread. If, then, the hand 
be held out towards the 
suspended electrified body, 
it will turn round and ap- 
proach the hand. So, 
again, a piece of silk rib- 
bon, if rubbed with warn) 



Boyle 




Fig. 2 



n 



indiarubber, or even if drawn between two pieces of 
warm flannel, and then held up by one end, will be 

found to be attracted 
by objects presented to 
it. If held near the 
wall of the room it will 
fly to it and stick to it. 
With proper precau- 
tions it can be shown 
that both the rubber 
and the thing rubbed 
are in an electrified 
state, for both will 
attract light bodies ; 
but to show this, care 
must be taken not to 
Thus, if it is desired to 





Fig. 3- 



handle the rubber too much, 
show that v/hen a piece of rabbit's fur is rubbed upon 
sealing-wax, the fur becomes also electrified, it is better 
not to take the fur in the hand, but to fasten it to the 



ELEMENTARY LESSONS ON Ichap. I. 



end of a glass rod as a handle. The reason of this 
precaution will be explained toward the cldse of this 
lesson, and more fully in Lesson IV. 

A large number of substances, including iron, gold, 
brass, and all the metals, when held in the hand 'ind 
rubbed, exhibit no sign of electrification, — that is to say, 
do not attract light bodies as rubbed amber and rubbed 
glass do. Gilbert mentions also pearls, marble, agate, 
and the lodestone, as substances not excited electrically 
by rubbing them. Such bodies were, on that account, 
formerly termed non-electrics ; but the term is erro- 
neous, for if they are fastened to glass handles and then 
rubbed with silk or fur, they behave as electrics. 

3. Electrical Repulsion. — When experimenting, 
as in Fig. i , with a rubbed glass rod and bits of chopped 
paper, or 'straw, or bran, it will be noticed that these 

little bits are first attracted 
and fly up towards the ex- 
cited rod, but that, having 
touched it, they are 
speedily repelled and fly 
back to the table. To 
show this repulsion better, 
let a small piece of feather 
or down be hung by a silk 
thread to a support, and 
let an electrified glass rod 
be held near it. It will 
dart towards the rod and 
stick to it, and a moment 
later will dart away from 
it, repelled by an invisible 
force (Fig. 4), nor will it 
again dart towards the rod. If the experiment be 
repeated with another feather and a stick of sealing-wax 
rubbed on flannel the same effects will occur. But, if 
now the hand be held towards the feather, it will rush 




Fig. 4. 



CHAP. I. J ELECTRICITY AND MAGNETISM. 



toward the hand, as the rubbed body in Fig. 3 did. 
This proves that the feather, though it has not itself 
been rubbed, possesses the property originally imparted to 
the rod by rubbing it. In fact, it has become electrified, 
by having touched an electrified body which has given 
part of its electricity to it. It would appear then that 
two bodies electrified with the same electricity repel one 
another. This may be confirmed by a further experi- 
ment A rubbed glass rod, hung up as in Fig. 3, is 
repelled by a similar rubbed glass rod ; while a rubbed 
stick of sealing-wax is repelled by a second rubbed stick 
of sealing-wax. Another way of showing the repulsion 
between two simi- 
larly electrified bodies 
is to hang a couple 
of small pith -balls, 
by thin linen threads 
to a glass support, 
as in Fig. 5, and 
then touch them both 
with a rubbed glass 
rod. They repel one 
another and fly apart, 
instead of hanging 
down side by side, 
while the near pre- 
sence of the glass rod will make them open out still 
wider, for now it repels them both. The self-repulsion 
of the parts of an electrified body is beautifully illustrated 
by the experiment of electrifying a soap-bubble, which 
expands when electrified. 

4. Two kinds of Electrification. — Electrified 
bodies do not, however, always repel one another. The 
feather which (see Fig. 4) has been touched by a rubbed 
glass rod. and which in consequence is repelled from 
the rubbed glass, will be ai traded if a stick of rubbed 
sealing-wax be presented to i*^ : and conversely, if the 




Fig. 5- 



6 ELEMENTARY LESSONS ON Ichap. i. 

feather has been first electrified by touching it with the 
rubbed seolijig-wax, it will be attracted to a rubbed glass 
rod, though repelled by the rubbed tvax. So, again, a 
rubbed glass rod suspended as in Fig. 3 will be attracted 
by a rubbed piece of sealing-wax, or resin, or amber, 
though repelled by a rubbed piece of glass. The two 
pith -balls touched (as in Fig. 5) with a rubbed glass 
rod fly from one another by repulsion, and, as we have 
seen, fly wider asunder when the excit^ glass rod is 
held near them ; yet they fall nearer together when a 
rubbed piece of sealing-wax is held under them, being 
attracted by it. Symmer first observed such phenomena 
as these, and they were independently discovered by Du 
Fay, who suggested in explanation of them that there 
were two different kinds of electricity which attracted 
one another while each repelled itself. The electricity 
produced on glass by rubbing it with silk he called 
vitreous electricity, supposing, though erroneously, that 
glass could yield no other kind ; and the electricity 
excited in such substances as sealing-wax, resin, shellac, 
indiarubber, and amber, by rubbing them on wool 01 
flannel, he termed resinous electricity. The kind ot 
electricity produced is, however, found to depend not only 
on the thing rubbed but on the rubber also ; for glass 
yields " resinous " electricity when rubbed with a cat's 
skin, and resin yields " vitreous " electricity if rubbed 
with a soft amalgam of tin and mercury spread on 
leather. Hence these names have been abandoned in 
favour of the more appropriate terms introduced by 
Franklin, who called the electricity excited upon glass by 
rubbing it with silk positive electricity, and that produced 
on resinous bodies by friction with wool or fur, negative 
electricity. The observations of Symmer and Du Fay may 
therefore be stated as follows : — Two positively electrified 
bodies repel one another: two negatively electrified bodies 
repel one another : but a positively electrified body and 
a negatively electrifled body attract one another. 



CHAP. I.] ELECTRICITY AND MAGNETISM. ? 

5. Simultaneous production of both Electrical 
States. — Neither kind of electrification is produced 
alone ; there is always an equal quantity of both kinds 
produced ; one kind appearing on the thing rubbed 
and an equal amount of the other kind on the rubber. 
The clearest proof that these amounts are equal can be 
given in some cases. For it is found that if both the - 
electricity of the rubber and the + electricity of the thing 
rubbed be imparted to a third body, that third body will 
show no electrification at all^ the two equal and opposite 
electrifications having exactly neutralised each other. 

In the following list the bodies are arranged in such 
an order that if any two be rubbed together the one 
which stands earlier in the series becomes positively 
electrifiea, and the one that stands later negatively 
electrified : — Fti}\ wool^ ivory ^ glassy silk^ metals^ sul- 
phur^ indiarubber^ gtdtapercha^ collodion. 

6. Theories of Electricity. — Several theories, have 
been advanced to account for these phenomena, but all 
are more or less unsatisfactory. Symmer proposed a 
'* t"wo-flLuid " theory, according to which there are two 
imponderable electric fluids of opposite kinds, which 
neutralise one another when they combine, and which 
exist combined in equal quantities in all bodies until 
their condition is disturbed by friction. A modification 
of this theory was made by Franklin, who proposed 
instead a " one-fluid " theory, according to which 
there is a single electric fluid distributed usually uniformly 
in all bodies, but which, when they are subjected to friction, 
distributes itself unequally between the rubber and the 
thing rubbed, one having more of the fluid, the other 
less, than the average. Hence the terms positive and 
negative^ which are still retained ; that body which is 
supposed to have an excess being said to be charged 
with positive electricity (usually denoted by the plus sign 
+ ), while that which is supposed to have less is said to 
be charged with negative electricity (and is denoted by 



8 ELEMENTARY LESSONS ON [chap. i. 

the minus sign - ). These terms are, however, purely 
arbitrary, for in the present state of science we do not 
know which of these two states really means more and 
which means less. It is, however, quite certain that 
electricity is not a material fluid^ whatever else it 
may be. For while it resembles a fluid in its property 
of apparently flowing from one point to another, it differs 
from every known fluid in almost every other respect. 
It possesses no weight ; it repels itself. -It is, moreover^, 
quite impossible to conceive of two fluids whose proper- 
ties should in every respect be the precise opposites of 
one another. For these reasons it is clearly misleading 
to speak of an electric fluid or fluids, however convenient 
the term may seem to be. Another theory, usually known 
as the molecular theory of electricity, and first dis- 
tinctly upheld by Faraday, supposes that electrical states 
are the result of certain peculiar conditions of the mole- 
cules of the bodies that have been rubbed, or of the 
"aether" which is believed to surround the molecules. 
The late discoveries of wireless telegraphy and X-rays, it is 
true, are based on these theories and become intelligible through 
them alone, but for convenience we shall, in these lessons, use 
the term electricity, regardless of theories. 

*7. Oharg^e. — The quantity of electrification of either 
kind produced by friction or other means upon the surface 
of a body is spoken of as a charge, and a body when 
electrified is said to be charged. It is clear that there 
may be charges of diilerent values as well as of either 
kind. When the charge of electricity is removed from 
a charged body it is said to be discharged. Good 
conductors of electricity are instantaneously discharged 
if touched by the hand or by any conductor in contact 
with the ground, tlie charge thus finding a means of 
escaping to earth. A body that is not a good conductor 
maybe leadily discharged by passing it rapidly through the 
flame of a spii it-lamp or a candle ; foi the flame instantly 
carries off the electricity and dissipates it in the air. 



CHAP. I.] ELECTRICITY AND MAGNETISM. 9 

Electricity may either reside upon the surface of bo^iies 
as a charge^ or flow through their substance as a 
current. That branch of the science which treats of 
the laws of the charges upon the surface of bodies is 
termed electrostatics, and is dealt with in Chapter 
IV. The branch of the subject which treats of the flow 
of electricity in currents is dealt with in Chapter II L, and 
other later portions of this book. 

8. Conductors and Insulators. — The term ** con- 
ductors," used above, is applied to those bodies which 
readily allow electricity to flow through them. Roughly 
speaking bodies may be divided into two classes — those 
which conduct and those which do not ; though very 
many substances are partial conductors, and cannot well 
be classed in either category. All the metals conduct 
well ; the human body conducts, and so does water. 
On the other hand glass, sealing-wax, silk, shellac, gutta- 
percha, indiarubber, resin, fatty substances generally, 
and the air, are "non-conductors." On this account 1 
these substances are used to make supports and handles 
for electrical apparatus where it is important that the 
electricity should not leak away ; hence they are some- 
times called insulators or isolators, Faraday termed 
them dielectrics. We have remarked above that Gil- 
bert gave the name of non-electrics to those substances 
which, like the metals, yield no sign of electrification when 
held in the hand and rubbed. We now know the reason 
why they show no electrification ; for, being good conduct- 
ors, the electricity flows away as fast as it is generated. 
The observation of Gilbert that electrical experiments 
fail in damp weather is also explained by the knowledge 
that water is a conductor, the film of moisture on the 
surface of damp bodies causing the electricity produced 
by friction to leak away as fast as it is generated. 

.9. Other electrical effects. — The production of 
electricity by friction is attested by other effects than 
those of attraction and repulsion, which hitherto v/e have 



10 ELEMENTARY LESSONS ON [chap, j 

^ ■ . ■ ■JU4W^ I " ' "■ ■'" I. . . I . , « .i , I I . < 1 ■ i ■ ' ■.— — ■ 

assumed to be the test of the presence of electricity. 
Olto von Guericke first observed that sparks and flashes 
of h'ght could be obtained from highly electrified bodies at 
the moment when they were discharged. Such sparks are 
usually accompanied by a snapping sound, suggesting on a 
small scale the thunder accompanying the lightning spark, 
as was remarked by Newton and other early observers. 
Pale flashes of light are also produced by the discharge 
of electricity through tubes partially exhausted of air by 
the air-pump. Other eflfects will be noticed in due course. 
10. Other Sources of Electrification. — The stu- 
dent must be remrinded that friction is by no means the 
only source of electricity. The other sources, per- 
cussion, compression, heat, chemical action, physiological 
action, contact of metals, etc., will be treated of in Lesson 
VI L We will simply remark here that friction between 
two different substances always produces electrical 
separation, no matter what the substances may be. 
Symmer observed the production of electricity when a 
silk stocking was drawn over a woollen one, though 
woollen rubbed upon woollen, or silk rubbed upon silk, 
produces no electrical effect. If, however, a piece of 
rough glass be rubbed on a piece of smooth glass, 
electrification is observed ; and indeed the conditions of 
the surface play a very important part in the production 
of electricity by friction. In general, of two bodies 
thus rubbed together, that one becomes negatively 
electrical whose particles are the more easily removed 
by friction. Differences of temperature also affect the 
electrical conditions of bodies, a warm body being usually 
negative when rubbed on a cold piece of the same sub- 
stance. Pdclet found the degree of electrification produced 
by rubbing two substances together to be independent of 
the pressure and of the size of the surfaces in contact, 
but depended on the materials and on the velocity v/ith 
which they moved over one another. Rolling friction 
and sliding friction produced equal effects. The quantity 



CHAP. I.] ELECTRICITY AND MAGNETISM iT 

of electrification produced is, however, not proportional 
to the amount of the actual mechanical friction ; hence 
it appears doubtful whether friction is truly the cause of 
the electrification Indeed, it is probable that the true 
cause is the contact of dissimilar substances (see Art. 
73), and that when on contact two particles have 
assumed opposite electrical states, one being + the 
other - , it is necessary to draw them apart before their 
respective electrifications can be observed. Electrical 
machines are therefore machines for bringing dissimilar 
substances into intimate contact, and then drawing apart 
the particles that have touched one another and become 
electrical. 

Lesson I L — Electroscopes. 

IL Simple -Electroscopes. — An instrument for 
detecting whether a body is electrified or not, and 
whether the electrification is positive or negative, is 
termed an Electroscope. The feather which was 
attracted or repelled, and the two pith balls which flew 
apart, as we. found in Lesson I., are in reality simple 
electroscopes. There are, however, a number of pieces 
of apparatus better adapted for this particular purpose, 
some of which we will describe. 

12. Straw-Needle Electroscope. — The earliest 
electroscope was that devised by Dr. Gilbert, and shown 
in Fig. 6, which consists of a stiff straw balanced lightly^ 




Fisr. 6. 



upon a sharp point. A thin strip of brass or wood, or 
even a goose quill, balanced upon a sewing needle, will 



12 



ELEMENTARY LESSONS ON [chap. i. 



serve equally well. When an electrified body is held near 
the electroscope it is attracted and turned round, and will 
thus 'indicate the presence of quantities of electricity far 
too small to attract bits of paper from a table. 

13. Gold-Leaf Electroscope. — A still more sensi- 
tive instrument is the Gold-Leaf Electroscope In- 
vented by Bennet, and shown in Fig. 7. We have 
seen how two pith -balls when similarly electrified repel 
one another and stand apart, the force of gravity being 
partly overcome by the force of the electric repulsion. 




Fig. 7. 

A couple of narrow strips of the thinnest tissue paper, 
hung upon a support, will behave similarly when electri- 
fied. But the best results are obtained with two strips 
of gold-leaf, which, being excessively thin, is much 
lighter than the thinnest paper. The Gold-Leaf Electro- 
scope is conveniently made by suspending the two leaves 
within a wide-mouthed glass jar, which both serves to 



CHAP. I.] ELECTRICITY AND MAGNETISM. 13 

protect them from draughts of ah: and to support them 
from contact with the ground. Through the cork, which 
should be varnished with shellac or with paraffin wax, is 
pushed a bit of glass tube, also varnished. Through this 
passes a stiff brass wire, the lower end of which is bent 
at a right angle to receive the two strips of gold-leaf, 
while the upper supports a flat plate of metal, or may be 
furnished with a brass knob. When kept dry and free 
from dust it will indicate excessively small quantities of 
electricity. A rubbed glass rod, even while two or three 
feet from the instrument, will cause the leaves to repel 
one another. The chips produced by sharpening a pencil, 
falling on the electroscope top, are seen to be electrified. 
If the knob be even brushed with a small camel's hair 
brush, the slight friction produces a perceptible effect. 
With this instrument all kinds of friction can be shown 
to produce electrification. Let a person, standing upon 
an insulating support, — such as a stool with glass legs, 
or a board supported on four glass tumblers, — be briskly 
struck with a silk handkerchief, or with a fox's tail, or 
even brushed with a clothes' brush, he will be electrified, 
as will be indicated by the electroscope if he place one 
hand on the knob at the top of it. The Gold-Leaf 
Electroscope can further be used to indicate the kind of 
electricity on an exjcited body. Thus, suppose we rubbed 
a piece of brown paper with a piece of indiarubber and 
desired to find out whether the electrification excited on 
the paper was + or — , we should proceed as follows : — 
First charge the gold leaves of the electroscope by 
touching the knob with a glass rod rubbed on silk. 
The leaves diverge, being electrified with + electrifi- 
cation. When they are thus charged the approach of 
a body which is positively electrified will cause them to 
diverge still more widely ; while, on the approach of one 
negatively electrified, they will tend to close together. 
If now the brown paper be brought near the electroscope, 
the leaves will be seen to diverge more, proving the 



'4 



ELEMENTARY LESSONS ON [chap, i 



electrification of the paper to be of the same kind as 
that ^\ith which the electroscope is charged, or positive. 
The Gold-Leaf Electroscope will also indicate roughly 
the anriount of electricity on a body placed in contact 
with it, for the gold leaves open out more widely when 
the quantity of electricity thus imparted to them is greater. 
For exact measurement, however, of the amounts of 
electricity thus present, recourse must be had to the instru- 
ments known as Electrometers, described in Lesson XXL 
In another form of electroscope (Bohnenberger's) a 
single gold leaf is used, and is suspended between two 
metallic plates, one of which can be positively, the other 
negatively electrified, by placing them in communication 
with the poles of a " dry pile " (Art. 182), If the gold 
leaf be charged positively or negatively it will be 
attracted to one side and repelled from the other, 
according to the law of attraction and repulsion men- 
tioned in Art. 4. 

14. Henley's Quadrant Electroscope. — The 
Quadrant Electroscope is sometimes employed as an 
indicator for large charges of electricity. It consists ol 
a pith ball at the end of a light 
arm fixed on a pivot to an upright. 
When the whole is electrified the 
pith-ball is repelled from the up- 
right and flies out at an angle, 
indicated on a graduated scale or 
quadrant behind it. Its usual foim 
is shown in Fig. 8. This little 
electroscope, which is seldom 
used except to show whether an 
electric machine or a Leyden 
battery is charged, must on no 
account be confused \nth the deli- 
cate ^* Quadrant Electrometer" desciibed in Lesson 
XXL, whose object is to jneasure veiy small charges 
of electricity — not to indicate large ones. 




Fig. 8. 



CHAP. I,] ELECTRICITY AND MAGNETISM. 



15 



15. The Torsion Balance. — Although more pro- 
perly^ an Electrometer than a mere Electroscope^ it 
will ^ be most convenient to describe here the instrument 
known as the Torsion 



Balance. (Fig. 9.) This 
instrument serves to 
measure the force of the 
repulsion between two 
similarly electrified 
bodies, by balancing the 
force of this repulsion 
against the force exerted 
by a fine wire in untwist- 
ing itself after it has been 
t\\isted. The torsion 
balance consists of a 
light arm or lever of 
shellac suspended within 
a C}4indrical glass case 




Fig. 9. 



by means of a fine silver wire. At one end this lever is 
furnished with a gilt pith-ball, n. The upper end of the 
siher wire is fastened to a brass top, upon which a circle, 
divided into degrees, is cut. This top can be turned 
round in the tube which supports it, and is known as the 
torsion-head. Through an aperture in the cover there 
can be introduced a second gilt pith -ball m^ fixed to 
the end of a vertical glass rod a. Round the glass case, 
at the level of the pith-balls, a circle is drawn, and 
divided also into degrees. 

In using the torsion balance to measure the amount 
of a charge of electricity, the following method is 
adopted : — First, the torsion-head is turned round until 
the t\\o pith-balls in and n just touch one another. 
Then the glass rod a is taken out, and the charge of 
electricity to be measured is imparted to the ball m^ 
which is then replaced in the balance. As soon as ;// 
and n touch one another, part of the charge passes from 



i6 ELEMENTARY LESSONS ON [chap, t 



m to ;/, and they repel one another because they are 
then similarly electrified. The ball ;/, therefore, is driven 
round and twists the wire up to a certain extent. The 
force of repulsion becomes less and less as n gets 
farther and farther from m; but the force of the twist 
gets greater and greater the more the wire is twisted. 
Hence these two forces will balance one another when 
the balls are separated by a certain distance, and it is 
dear that a large charge of electricity will repel the ball 
n with a greater force than a lesser charge would. 
The distance through which the ball is repelled is read 
off not in inches but in angular degrees of the scale. 
When a wire is twisted, the force with which it tends to 
Untwist is precisely proportional to the amount of the 
twist. The force required to twist the wire ten degrees 
is just ten times as great as the force required to twist 
it one degree. In other words, the force of torsion is 
proportional to the angle of torsion. The angular 
distance between the two balls is, when they are not 
very widely separated, very nearly proportional to the 
actual straight distance between them, and represents 
the force exerted between electrified balls at that 
distance apart. The student must, however, carefully 
distinguish between the measurement of the force and 
the measurement of the actual quantity of electricity 
with which the instrument is charged. For the fotce 
exerted between the electrified balls will vary at different 
distances according to a particular law known as the 
" law of inverse squares," which requires to be carefully 
explained. 

16. The Law of Inverse Squares. — Coulomb 
proved, Ly means of the Torsion Balance, that the force 
exerted between two small electrified bodies varies 
inversely as the square of the distance between them 
when the distance is varied. Thus, suppose two electri- 
fied bodies one inch apart repel one another with a 
certain force, at a distance of two inches the force will 



CHAP. I.] ELECTRICITY AND MAGNETISM. ry 



be found to be only one quarter as great as the force 
at one inch ; and at ten inches it will be only ~ th 
part as great as at one inch. This law is proved by the 
following experiment with the torsion balance. The 
two scales were adjusted to o°, and a certain charge was 
then imparted to the balls. The ball n was repelled 
round to a distance of 36°. The twist on the wire 
between its upper and lower ends was also 36°, or the 
force of the repulsion was thirty-six times as great as the 
force required to twist the wire by 1°, The torsion-head 
was now turned round so as to twist the thread at the 
top and force the ball n nearer to m^ and was turned 
round until the distance between n and m was halved. 
To bring down this distance from 36^ to 18^, it was 
found needful to twist the torsion-head through 126''. 
The total twist between the upper and lower ends of the 
wire was now 126° -v 18**, or 144°; and the force was 
144 times as great as that force which would twist the 
wire 1°. But 144 is four times as great as 36 ; hence 
we see that while the distance had been reduced to one 
half^ the force between the balls had become four 
times as great. Had we reduced the distance to one 
quarter^ or 9°, the total torsion would have been found 
to be 57 6°, or sixteen times as great ; proving the 
force to vary inversely as the square of the 
distance. 

In practice it requires great experience and skill to 
obtain results as exact as this, for there are many 
sources of inaccuracy in the instrument. The balls 
must be very small, in proportion to the distances between 
them. The charges of electricity on the balls are found, 
moreover, to become gradually less and less, as if the 
electricity leaked away into the air. This loss is less 
if the apparatus be quite dry. It is therefore usual to 
dry the interior by placing inside the case a cup con- 
taining either chloride of calcium, or pumice stone 
soaked with strong sulphuric acid, to absorb the moisture, 



58 ELEMENTARY LESSONS ON [chap. i. 

Before leaving the subject of electric forces, it may be 
well to mention that the force of aitracilon between 
two oppositely electrified bodies varies also inversely as 
the square of the distance between them. And in every 
case, whether of attraction or repulsion, the force at any 
given distance Is proportional to the product of the 
two quantities of electricity on the bodies. Thus, if 
we had separately given a charge of 2 to the ball 7n and 
a charge of 3 to the ball ;/, the force between them will 
be 3x2^6 times as great -as if each had had a 
charge of i given to it. 

17. Unit quantity of Electricity. — In conse- 
quence of these laws of attraction and repulsion, it is 
found most convenient to adopt the following definition 
for that quantity of electricity which we take for a unit or 
standard by which to measure other quantities of elec- 
tricity. One Unit of Electricity is that quaniiiy which^ 
mhen placed at a distance of one centimetre in air from 
a similar and equal quantity^ repels it with a force of 
03ie dyne. Further information about the measure- 
ment of electrical quantities is given in Lessons XX. 
and XXI 



Lesson III. — Electrification by Induction, 

18. We have now learned how two charged bodies 
may attract or repel one another. It is sometimes said 
that it is the electricities in the bodies which attract or 
repel one another ; but as electricity is not known to 
exist except in or on material bodies, the proof that it 
is the electricities themselves which are attracted is only 
indirect. Nevertheless there are certain matters which 
support this view, one of these being the electric influ- 
ence exerted by an electrified body uDon one not 
electrified. 

Suppose we rub a ball of glass with silk to electrify it, 



CHAP. I.] ELECTRICITY AND MAGNETISM. 



19 



and hold it near to a body that has not been electrified, 
what will occur? W:e take for this experiment the 
apparatus shown in Fig. 10, consisting of a long 
sausage -shaped piece of metal, either hollow or solid, 
held upon a glass support. This "conductor," so called 
because it is made of metal which permits electricity to 
pass freely through it or over its surface, is supported on 
glass to prevent the escape of electricity to the earth, 
glass being a. non-conductor. The presence of the 
positive electricity of the glass ball near this conductor 
is found to induce electricity on the conductor, which. 





Fig. 10. 



although it has not been rubbed itself, will be found to 
behave at its two ends as an electrified body. The 
ends of the conductor will attract little bits of paper ; 
and if pith -balls be hung to the ends they are found 
to be repelled. It will, however, be found that the 
middle region of the long -shaped conductor will give 
no sign of any electrification. Further examination will 
show that the two electrifications on the ends of the con- 
ductor are of opposite kinds, that nearest the excited 
glass ball bemg a negative charge, and that at the 
farthest end beins: an eaual charge, but of positive 



ELEMENTARY LESSONS ON [chap. l. 

20 

Signr It appears then that a positive charge attracts 
negative and repels positive, and that this influence can 
be exerted at a distance from a body. If we had begun 
with a charge of negative electrification upon a stick of 
sealing-wax, the presence of the negative charge near the 
conductor would have induced a positive charge on the 
near end, and negative on the far end. This action, 
discovered in 1753 by John Canton, is spoken of as 
electric induction, or influence. It Vill take place 
across a considerable distance. Even if a large sheet 
of glass be placed between, the same effect will be 
produced. When the electrified body is removed both 
the charges disappear and leave no trace behind, and 
the glass ball is found to be just as much electrified as 
before ; it has parted with none of its own charge. It 
will be remembered that on one theory a body charged 
positively is regarded as having more -electricity than 
the things round it, while one with a negative charge 
is regarded as having less. According to this view 
it would appear that when a body (such as the + 
electrified glass ball) having more electricity than 
things around it is placed near an insulated conductor^ 
the uniform distribution of el-ectricity in that conductor 
is disturbed, the electricity flowing away from that end 
which is near the + body, leaving less than usual at 
that end, and producing more than usual at the other 
end. This view of things will account for the disapjiear- 
ance of all signs of electrification when the electrified 
body is removed, for then the conductor returns to its 
former condition ; and being neither more nor less elec- 
trified than all the' objects around on the surface of the 
earth, will show neither positive nor negative charge. 

19. ,If the conductor be made in two parts, so that 
while under the inductive influence of the electrified 
body they can be separated, then on the removal of the 
electrifieid body the two charges can no longer return 
[to neutralise one* another, but remain each on their own 



CHAP. Li ELECTRICITY AND MAGNETISM. 2! 

portion of tho conductor, and may be examined al 
4eisure. 

If the conductor be not insulated on glass supports, 
but placed in contact with the ground, that end only 
which is nearest the electrified body will be found to be 
electrified. The repelled electricity is indeed repelled 
as far as possible — into the earth. One kind of elec- 
trification only is under these circumstances to be found, 
namely, the opposite kind to that of the excited body, 
whichever this may be. The same effect occurs in this 
case as if an electrified body had the power of attracting 
up the opposite kind of charge out of the earth, though 
the former way of regarding matters is more correct. 

The quantity of the two charges thus separated by 
induction on such a conductor in the presence of a 
charge of electricity, depends upon the amount of the 
charge, and upon the distance of the charged body from 
the conductor. A highly electrified glass rod will 
produce a greater inductive effect than a less highly 
electrified one ; and it produces a greater effect as it is 
brought nearer and nearer. The utmost it can do will 
be to induce on the near end a negative charge equal 
in amount to its own positive charge, and a similar 
amount of positive electricity at the far end ; but usually, 
before the electrified body can be brought so near as to 
do this, something else occurs which entirely alters the 
condition of things. As the electrified body is brought 
nearer and nearer, the charges of opposite sign on the 
two opposed surfaces attract one another more and 
more strongly and accumulate more and more densely, 
until, as the electrified body approaches very near, a spark 
is seen to dart across, the two charges thus rushing 
together to neutralise one another, leaving the induced 
charge of positive electricity, which was formerly repelled 
to the other end of the conductor, as a permanent charge 
after the electrified body has been removed. 

20, We are now able to apply the principle of 




22 ELEMENTARY LESSONS ON [chap, i 

induction to explain why an electrified body should 
attract things that have not been electrified at all. Let 
a light ball be suspended by a silk thread (Fig. 1 1), and 
a rubbed glass rod held near it. The positive charge 
of the glass will induce a negative charge on the near side, 

and an equal amount of posi- 
tive electrification on the farther 
side, of the ball. The nearer 
half of the ball will therefore 
be attracted, and the farther 
half repelled; but the attraction 
p. ^^ will be stronger than the repul- 

^^' "* sion, because the attracted elec- 

tricity is nearer than the repelled. Hence on the whole 
the ball will be attracted. It can easily be observed 
that if a ball of non-conducting substance, such as wax, 
be employed, it is not attracted so much as a ball of 
conducting material. This in itself /troves that induction 
really precedes attraction, 

21. luduotive capacity. — We have assumed up to 
this point vthat electricity could act at a distance, and 
could produce these effects of induction without any 
intervening means of communication. This, however, 
is not the case, for Faraday discovered that the air in 
between the electrified body and the conductor played a 
very important part in the production of these actions. 
Had some other substance, such as paraffin oil, or solid 
sulphur, occupied the intervening space, the effect pro- 
duced i3y the presence of the electrified body at the 
same distance would have beeri greater. The power of 
a body thus to allow the inductive influence of an 
electrified body to act across it is called its inductive 
capacity (see Article 49 and Lesson XXII.) 

22. The Blectrophonis.— We are now prepared 
to explain the operation of a simple and ingenidus 
instrument, devised by Volta in 1775, for the purpose 
of procuring^ by the principle of induction, an unlimited 



CHAP. I.] ELECTRICITY AND MAGNETISM. 



23 



number of charges of electricity from one single charge. 
This instrument is the Eleotrophorus (Fig. 12). It 
consists of two parts, a round cake of resinous material 
cast in a metal dish or "sole," about 12 inches in 
diameter, and a round disc of slightly smaller diameter 
made of metal, or of wood covered with tinfoil, and 







liiiilB^^^ 



X'lg. 12 

provided with a glass handle. Shellac, or sealing-wax, 
or a mixture of resin, shellac, and Venice turpentine, may 
be used to make the cake. A slab of sulphur will 
also answer, but it is liable to crack. Sheets of hard 
ebonised indiarubber are excellent ; but the surface of 
this substance requires occasional washing with ammonia 
and rubbing with paraffin oil, as the sulphur contained 



24. ELEMENTARY LESSONS ON [chap. i. 

in It is liable to oxidise and to attract moisture. To use 
the electrophorus the resinous cake must be beaten or 
rubbed with a warm piece of woollen cloth, or, better 
still, with a cat's skin. The disc or ^* cover " is then 
placed upon the cake, touched momentarily with the 
finger, then removed by taking it up by the glass handle, 
when it is found to be powerfully electrified with a posi- 
tive charge, so much so indeed as to yield a spark when 
the knuckle is presented to it. The '^ cover " may be 
replaced, touched, and once more removed, and will 
thus yield any number of sparks, the original charge on 
the resinous plate meanwhile remaining practically as 
strong as before. 



vQ 

















■^ 




-f + 


-t 


■t- 


t 


+ 


+ 


■t 


f 














1 



Fig. 13. Fig. 14. 

The theory ot the electrophorus is ver^'' simple, pro- 
vided the student, has clearly grasped the principle of 
induction explained above. When the resinous cake 
is first beaten with the cat's skin its surface is negatively 
electrified, as indicated in Fig. 13. When the metal 
disc is placed down upon it, it rests really only on three 
or four points of the surface, and may be regarded as an 
insulated conductor in the presence of an electrified 
body. The negative electrification of the cake therefore 
acts inductively on the metallic disc or '' cover," attract- 
ing a positive charge to its under side, and repelling 
a negative charge to its upper surface. This state 
of things is shown in Fig. 14. If now. the cover be 
touched for an instant with the finger, the negative 
charge of the upper surface (which is upon the upper 



CHAP, r.j ELECTRICITY AND MAGNETISM, 25 

surface being repelled by the negative charge on the cake) 
will be neutralised by electricity flowing in from the 
earth through the hand and body of the experimenter. 
The attracted positive charge will, however, remain, being 
bound as it were by its attraction towards the negative 
chai'ge on the cake. Fig, 1 5 shows the condition of 
things after the cover has been touched. If, finally, the 
cover be lifted by its handle, the remaining positive 
charge will be no longer "bound" on the lower surface 
by attraction, but will distribute itself on both sides of 



r 



4--h-h-h-h-h-H4- 




1 C 



Fig. 15. Fig. 16. 

the cover, and may be used to give a spark, as already 
said. It is clear that no part of the original charge has 
been consumed in the process, which may be repeated 
as often as desired. As a matter of fact, the charge on 
the cake slowly dissipates — especially if the air be damp. 
Hence it is needful sometimes to renew the original 
charge by afresh beating the cake with the cat's skin. 
The labour of touching the cover with the finger at each 
operation may be saved by having a pin of brass or a 
strip of tinfoil projecting from the metallic *' sole " on to 
the top of the cake, so that it touches the plate each 
time, and thus neutralises the negative charge by allow- 
ing electricity to flow in from the earth. 

Since the electricity thus yielded by the electrophorus 



26 ELEMENTARY LESSONS ON [chap, i 



is not obtained at the expense of any part of the original 
charge, it is a matter of some interest to inquire what 
the source is from which the energy of this apparently 
unlimited supply is drawn ; for it cannot be called 
into existence without the expenditure of some other 
form of energy, any more than a steam-engine can work 
without fuel. As a matter of fact it is found that it 
is a little harder work to lift up the cover when it 
is charged with the + electricity than if it were not 
charged ; for, when charged, there is the force of the 
electric attraction to be overcome as well as the force 
of gravity. Slightly harder work is done at the ex- 
pense of the muscular energies of the operator ; and this 
is the real origin of the energy stored up in the separate 
charges. 

23. Continuous Electrophori. — The purely me- 
chanical actions of putting down the disc on to the 
cake, touching it, and lifting it up, can be performed 
automatically by suitable mechanical arrangements, 
which render the production of these inductive charge3 
practically continuous. The earliest of such contin- 
uous electrophori was Bennet's '^ Doubler," the latest 
is Wimshurst's machine, described in Lesson V. 

24. " Free " and " Bound " Electricity. — We 
have spoken of a charge of electricity on the surface of 
a conductor, as being " bound " when it is attracted by 
the presence of a neighbouring charge of the opposite 
kind. The converse term " free " is sometimes applied 
to the ordinary state of electricity upon a charged con- 
ductor, not in the presence of a charge of an opposite 
kind. A ^^free^^ charge upon an insulated conductoi 
flows away instantaneously to the earth, if a conducting 
channel be provided, as will be explained in the next 
lesson. It is immaterial what point of the conductor be 
touched. Thus, in the case represented in Fig. lo, 
wherein a + electrified body induces — electrification at 
the near end, and -f electrification at the far end of afi 



CHAP. I.] ELECTRICITY AND MAGNETISM. 27 

insulated conductor, the — charge is " bound," being 
attracted, while the -f charge at the other end, being 
repelled, is *'free"; and if the insulated conductor be 
touched by a person standing on the ground, the "free" 
electricity will flow away to the earth through his body, 
while the *' bound " electricity will remain, no matter 
whether he touch the conductor at the far end, or at the 
near end, or at the middle. 

26. Inductive method of charging the G-old- 
leaf Electroscope. — The student will now be prepared 
to understand the method by which a Gold-Leaf Electro- 
scope can be charged with the opposite kind of charge to 
that of the electrified body used to charge it. In Lesson 
II. it was assumed that the way to charge an electro- 
scope was to place the excited body in contact with the 
knob, and thus permit, as it were, a small portion of the 
charge to flow into the gold leaves. A rod of glass 
rubbed on silk being + would thus obviously impart + 
electrification to the gold leaves. 

Suppose, however, the rubbed glass rod to be held a 
few inches above the knob of the electroscope, as is 
indeed shown in Fig. 7. Even at this distance the gold 
leaves diverge, and the effect is due to induction. The 
gold leaves, and the brass wire and knob, form one con- 
tinuous conductor, insulated from the ground by the 
glass jar. The presence of the + electricity of the 
glass acts inductively on this ^' insulated conductor," 
inducing - electrification on the near end or knob, and 
inducing -f at the far, end, i\e,, on the gold leaves, 
which diverge. Of these two induced charges, the - 
on the knob is "bound," while the + on the leaves is 
*' free." If now, while the excited rod is still held above 
the electroscope, the knob be touched by a person 
standing on the ground, one of these two induced charges 
flows to the ground, namely the free charge^— not that 
on the knob itself, for it was *^ bound," but that on the 
gold leaves which was "free" — and the gold leaves 



28 ELEMENTARY LESSONS ON [chap, i 



instantly drop down straight. There now remains only 
the - charge on the knob, " bound " so long as the 
4- charge of the glass rod is near to attract it. But 
if, finall)-, the glass rod be taken right away, the ~ 
charge is no longer " bound " on the knob, but is 
^^ free " to flow into the leaves, which once more diverge 
— but this time with a Jiegative electrification. 

26. " Tho Return-Shock." — It is sometimes noticed 
that, when a charged conductor is suddenly discharged, 
a discharge is felt by persons standing near, or may 
even affect electroscopes, or yield sparks. This action, 
known as the " return-shock,'' is due to induction. For 
in the presence of a charged conductor a charge of 
opposite sign will be induced in neighbouring bodies, 
and on the discharge of the conductor these neighbour- 
ing bodies may also suddenly discharge their induced 
charge into the earth, or into other conducting bodies. 
A ** return-shock " is sometimes felt by persons standing 
on the ground at the moment when a flash of lightning 
has struck an object some distance away. 



Lesson IV. — Conduct io7i aiid Disi7'ihttton of Electricity, 

27. Conduction. — Toward the close of Lesson 11 
we explained how certain bodies, such as the metals, 
conduct electricity, while others are non-conductors or 
insulators. This discovery is due to Stephen Gray ; 
who, in 1729, found that a cork, inserted into the end 
of a rubbed glass tube, and even a rod of wood stuck 
into the cork, possessed the power of attracting light' 
bodies He found, similarly, that metallic wire and pack- 
thread conducted electricity, while silk did not. 

We may repeat these experiments by taking (as in 
Fig. 17) a glass rod, fitted \Yith a cork and a piece of 
wood. If a bullet or a brass knob be hung to the end of 
this by a linen thread or a wire, it is found that when the 



CHAP. I.] ELECTIUCITY AND MAGNETISM. 



29 



glass tube is rubbed the bullet acquires the property of 
attracting light bodies. If a dry silk thread Ts used, 
however, no electricity will flow down to the bullet. 

Gray even succeeded in transmitting a charge of 
electricity through a hempen thread over 700 feet long, 
suspended on silken loops. A little later Du Fay 
succeeded in sending electricity to no less a distance 
irhan 1256 feet through a moistened thread, thus proving 
the conducting power of moisture From that time the 
classification of bodies into conductors and insulators 
has been observed. 




Fig. 17 

This distinction cannot, however, be entirely main- 
tained, as a large class of substances occupy an inter- 
mediate ground as partial conductors. For example, dry 
wood is a bad conductor and also a bad insulator ; it 
is a good enough conductor to conduct away the high- 
potential electricity obtained by friction ; but it is a 
bad conductor for the relatively low-potential electricity 
of small voltaic batteries. Substances that are very bad 
conductors are said to offer a great resistance to the 



30 



ELEMENTARY LESSONS ON [chap* I 



flow of electricity through them. There is indeed no 
substance so good a conductor as to be devoid of resist- 
ance. There is no substance of so high a resistance as 
not to conduct a little. Even silver, which conducts best 
of all known substances, resists the flow of electricity to 
a small extent ; and, on the other hand, such a non-con- 
ducting substance as glass, though its resistance is many 
million times greater than that of any metal, allows a 
small quantity of electricity to pass through it. In the 
following list, the substances named are placed in order, 
each conducting better than those lower down on the list 

Silver 



Good Conductors. 



Partial Conductors. 



Copper . 
Other metals 
Charcoal . 
Water . 
The body 
Cotton . 
Dry Wood 
Marble . 
Paper 
Oils 

Porcelain 
Wool . 
Silk 
Resin 

Guttapercha 
Shellac . 
Ebonite • 
Paraffin .- 
Glass 
Dry air . 

A simple way of observing experimentally whether a 
body is a conductor or not, is to take a charged gold- 
leaf electroscope, and, holding the substance to be 
' examined in the hand, touch the knob of the electro- 
scope with it. If the substance is a conductor the 
electricity will flow away through it arid through the 
body to the earth, and the electroscope will be discharged. 
Through good conductors the rapidity of the flow is so 



Non-Conduetors or 
Insuliators. 



CHAP. I.J ELECTRICITY AND MAGNETISM. 31 



great that tJae discharge is practically instantaneous. 
Further information on this Question is given in Lesson 

xxin. 

28. Distribution of Electricity on Bodies. — It 
electricity is produced at one part of a non-coiiductin<i 
body, it remains at that point and does not flow over 
the surface, or at most flows over it excessively slowly. 
Thus if a glass tube is rubbed at one end, only that one 
end is electrified. If a warm cake of resin be rubbed at 
one part with a piece of cloth, only the portion nibbed 
will attract light bodies. The case is, however, wholly 
different when a charge of electricity is impaited to any 
part of a conducting body placed on an insulating 
support, for it instantly distributes itself all over the 
surface, though in general not uniformly over all points 
of the surface. 

29. The Charge resides on the surface. — A 
charge of electricity resides only on the surface of 
conducting bodies. This is proved by the fact that it 
is found to be immaterial to the distribution what the 
interior of a conductor is made of; it may be solid metal, 
or hollow, or even consist of wood covered with tinfoil 
or gilt, but, if the shape be the same, the charge will 
distribute itself precisely in the same manner over the 
surface. There are also several ways of proving by 
direct experiment this very important fact. Let a hollow 
metal ball, having an aperture at the top, be taken (as in 
Fig. 18), and set upon an insulating stem, and charged 
by sending into it a few sparks from an electrophorus. 
The absence of any charge in the interior may be shown 
as follows : — In order to observe the nature of the 
electricity of a charged body, it is convenient to have 
some means of removing a small quantity of the charge 
as a sample for examination. To obtain such a sample, 
a little instrument known as a proof-plane is employed 
It consists of a little disc of sheet copper or of gilt paper 
fixed at the end of a small glass rod. If this disc is laid 



32 



ELEMENTARY LESSONS ON [chat i. 



on the surface of an electnned body at any point, part 
of the electricity flows into it, and it may be then re- 
moved, and the sample thus obtained may be examined 
with a Gold-leaf Electroscope in the ordinary way. For 
some purposes a metallic bead, fastened to the end of a 
glass rod, is more convenient than a flat disc. If such 




Fig. i8. 

a proof-plane be applied to the outside of our electrified 
hollow ball, and then touched on the knob of an electro- 
scope, the gold leaves will diverge, showing the presence 
of a charge. But if the proof-plane be carefully inserted 
through the opening, and touched against the inside of 



CHAP. I.J ELECTRICITY AND MAGNETISM. 



33 



the globe and then withdrawn, it will be found that the 
inside is destitute of electricity. An electrified pewter 
mug will show a similar result, and so will even a 
cylinder of gauze wire. 

30. Biot*s experiment. — Biot proved the same fact 
in another way. A copper ball was electrified and 
insulated. Two hollow hemispheres of copper, of a 
larger size, and furnished with glass handles, were then 
placed together outside it (Fig. 19). So long as they 
did not come into contact the charge remained on the 



A 




Fig. 19. 

inner sphere ; but if the outer shell touched the inner 
sphere for but an instant, the whole of the electricity 
passed to the exterior ; and when the hemispheres were 
separated and removed the inner globe was found to be 
completely discharged. 

31. Further explanation. — Doubtless the explana- 
tion of this behaviour of electricity is to be found in 
the property previously noticed as possessed by either 
kind of electricity, namely, that of repelling itself; hence 
it retreats as far as can be from the centre and remains 



34 



ELEMENTARY LESSONS ON [chap, t. 



upon the surface. An important proposition concerning 
the absence of electric force within a closed conductor is 
proved in Lesson XX. , meanwhile it must be noted that 
the proofs, so far, are directed to demonstrate the 
absence of a free charge of electricity in the interior 
of hollow conductors. Many other experiments have 
been devised in proof. Thus, Terquem showed that 
a pair of gold leaves hung inside a wire cage could 
not be made to diverge when the cage was elec- 
trified. Faraday constructed a conical bag of linen- 





Fig. 20. 

gauze, supported as in Fig. 20, upon an insulating 
stand, and to which silk strings were attached, by which 
it could be turned inside out. It was charged, and 
the charge was shown by the proof, plane and electro- 
scope to be on the outside of the bag. On turning it 
inside out the electricity was once more found outside. 
Faraday-s most striking experiment was made with a 
hollow cube, measuring 1 2 feet each way, built of wood, 
covered with tinfoil, insulated, and charged with a 
powerful machine, so that large sparks and brushes 



CHAP. I.J ELECTRICITY AND MAGNETISM. 35 

were darting off from every part of its outer surface. 
Into this cube Faraday took his most delicate electrov 
scopes ; but once within he failed to detect tht least 
influence upon them. 

32. AppUcations. — ^Advantage is taken of this in 
the construction of delicate electrometers and other 
instnunents, which can be effectually screened from 
the influence of electrified bodies by enclosing them 
in a thin metal cover, closed all round, except where 
apertures must be made for purposes of observation. It 
has also been proposed by the late Prof. Clerk Maxv/ell 
to protect buildings from lightning by covering them 
on the exterior with a network of wires. 

33. Apparent Exceptions. — There are two ap- 
parent exceptions to the law that electricity resides only 
on the outside of conductors, (i) If there are electrified 
insulated bodies actually placed inside the hollow con- 
ductor, the presence of these electrified bodies acts in- 
ductively and attracts the opposite kind of electricity to 
the inner side of the hollow conductor. (2) When 
electricity flows in a current, it passes, according to the 
latest theories, through the medium surrounding the 
conductor. Thus the law is limited to statical charges. 

34. Faradasr's *' Ice-pail " Bxpeiiment. — One ex- 
periment of Faraday deserves notice, as showing the 
part played by induction in these phenomena. He 
gradually lowered a charged metallic ball into a hollow 
conductor connected by a wire to a gold-leaf electro- 
scope (Fig. 21), and watched the effect. A pewter ice- 
pail being convenient for his purpose, this experiment is 
continually referred to by this name, though any other 
hollow conductor — a tin canister or a silver mug, placed 
on a glass support — would of course answer equally 
well. The following effects are observed: — Suppose 
the ball to have a -|- charge : as it is lowered into the 
hollow conductor the gold leaves begin to diverge, for 
the presence of the charge acts inductively, and attracts 



36 



ELEMENTARY LESSOxXS ON [chap. i. 



a ^ charge into the interior and repels a -l- charge to the 
exterior. The gold leaves diverge more and more until 
the ball is right within the hollo vv^ conductor, after which 
no greater divergence is obtained. On letting the ball 
touch the inside the gold leaves still remain diverging 
as before, and if now the ball is pulled out it is found 
to have lost all its electricity. The fact that the gold 




Fig. 21. 



leaves diverge no v/ider 
after the ball touched 
than they did just 
before, proves that 
when the charged ball 
is right inside the 
hollow conductor the 
induced charges are 
each of them precisely 
equal in amount to 
its own charge, and the 
interior negative charge 
exactly neutralises the 
charge on the ball at 
the moment when they 
touch, leaving the equal 
exterior charge un- 
changed. An electric 



cagej such as this ice-pail, when connected with an 
electroscope or electrometer, affords an excellent means 
of examining the charge on a body small enough to be 
hung inside it. For without using up any of the charge 
of the body (which we are obliged to do when applying 
the method of the proof-plane) we can examine the 
induced charge repelled to the outside of the cage, 
which is equal in amount and of the same sign. 

35. Distribution of Oharg'e. — A charge of elec 
tricity is not usually distributed uniformly over the 
surfaces of bodies. Experiment shows that there is 
more electricity on the edges an€l corners of bodies than 



CHAP. I.] ELECTRICITY AND MAGNETISM. 



37 



upon their flatter parts. This distribution can be de- 
duced from the theory laid down in Lesson XX., but 
meantime we will give some' of the chief cases as they 
can be shown to exist. The term Electric Density is 
used to signify the amount of electricity at any point of 
a surface ; t/ie electric density at a point is the fitnnber 
of units of electricity per tmit of area {i.e. per square 
inch, or per-^quare centimetre), the distribution being 
supposed uniform over this small surface. 

(a) Sphere. — The distribution of a charge over an 
insulated sphere of conducting material is uniform, 
provided the sphere is remote from the presence of all 
other conductors and all other electrified bodies ; or, in 




Fig. 22. 

Other words, the density is uniform all over it. This is 
symbolised by the dotted line round the sphere in Fig. 
22, <^, which is at an equal distance from the sphere all 
roundj suggesting an equal thickness of electricity at 
every point of the surface. It must be remembered 
that the charge is not really of any perceptible thickness 
at all ; it resides on or at the surface, but cannot be 
said to form a stratum upon it. 

(b) Cylinder with rounded ends. — Upon an 
elongated conductor, such as is frequently employed in 
electrical apparatus, the density is greatest at the ends 
where the curvature of the surface is the greatest. 



38 ELEMENTARY LESSONS ON [chav. i. 

(o) Two Spheres in contact. — Tf two splieres in 
contact with eacli other are insulated and charged, it is 
found that the density is greatest at the parts farthest 
from the point of contact, and least in the crevice 
between them. If the spheres are of unequal sizes 
the density is greater on the smaller sphere, which has 
the surface more curved. On an eg"g-shaped or pear- 
shaped conductor the density is greatest at the small 
end. On a cone the density is greatest at the apex ; 
and if the cone terminate in a sliarp point the density 
there is very much greater than at any other point. At 
a point, indeed, the density of the collected electricity 
may be so gieat as to electrify the neighbouring particles 
of air, which then are repelled, thus producing a con- 
tinual loss of charge. For this reason points and sharp 
edges are always avoided on electrical apparatus, except 
where it is specially desired to set up a discharge. 

(d) Flat Disc. — The density of a charge upon a 
flat disc is greater, as we should expect, at the edges 
than on the flat surfaces; but over the flat surfaces the 
distribution is fairly uniform. 

These various facts are ascertained by applying a 
small proof- plane successively at various points of the 
electrified bodies and examining the amount taken up by 
the proof-plane by means of an electroscope or electro- 
meter. Coulomb, who investigated mathematically as 
well as experimentally many of the important cases of 
distribution, employed the torsion balance to verify his 
calculations. He investigated thus the case of the 
ellipsoid of revolution, and found the densities of the 
charges at the extremities of the axis to be pioportional 
to the lengths of those axes. He also showed that the 
density of the charge at any other point of the surface of 
the ellipsoid was proportional to the length of the per- 
pendicular drawTi from the centre to the tangent at that 
point. Riess also investigated several interesting cases 
of distribution. He found the density at the middle of 



CHAP. I.] ELECTRICITY AND MAGNETISM. 39 

the edges of a cube to be nearly two and a half times 
as great as the density at the middle of a face ; while 
the density at a corner of the cube was more than four 
times as great. 

36. Redistribution of Charge. — If any portion 
of the charge of an insulated conductor be removed, the 
remainder of the charge will immediately redistribute 
itself over the surface in the same manner as the original 
charge, provided it be also isolaled, i,e.^ that no other 
conductors or charged bodies be near to perturb the 
distribution by complicated effects of induction. 

If a conductor be charged with any quantity of elec- 
tricity, and another conductor of the same size and shape 
(but uncharged) be brought into contact with it for an 
instant and then separated, it will be found that the 
change has divided itself equally between them. In the 
same way a charge may be divided equally into three or 
more parts by being distributed simultaneously over three 
or more equal and similar conductors brought into contact. 

If two equal metal balls, suspended by silk strings, 
charged with unequal quantities of electricity, are 
brought for an instant into contact and then separated, 
it will be found that the charge has redistributed itseli 
fairly, half the sum of the two charges being now the 
charge of each. This may even be extended to the 
case of charges of opposite signs. Thus, suppose two 
similar conductors to be electrified, one with a positive 
charge of 5 units and the other with 3 units of negative 
charge, when these are made to touch and separated, 
each will have a positive charge of i unit ; for the 
algebraic sum of + 5 and — 3 is + 2, which, shared 
between the two equal conductors, leaves + i for each. 

37. Capacity of Conductors. — If the conductors 
be unequal in size, or unlike in form, the shares taken 
by each in this redistribution will not be equal, but 
will be proportional to the electric capacities of the 
conductors. The definition of capacity in its relation 



40 ELKMfilNTARY LESSONS ON [chap, i 



lo electric quantities is given in Lesson XX., Art. 246. 
We may, however, make the remark, that two insulated 
conductors of the same form, but of different sizes, differ 
in their electrical capacity ; for the larger one must 
have a larger amount of electricity imparted to it in 
order to electrify its surface to the same degree. The 
term polenfial is employed in this connection, in the 
following way : — A given quantity of electricity will 
electrify an isolated body up to a certain " potential " 
(or power of doing electric work) depending on its 
capacity. A large qttantity of electricity imparted to a 
conductor of small capacity will electrify it up to a 
very high potential j just as a large quantity of water 
poured into a vessel of narrow capacity will raise the 
surface of the water to a high level in the vessel. The 
exact definition of Potential, in terms of energy spen*^ 
against the electrical forces, is given in the Lesson on 
Electrostatics (Art. 237). 

It will be found convenient to refer to a positively 
electrified body as one electrified to a 'positive or high 
potential J while a negatively electrified body n\ay be 
looked upon as one electrified to a low or negative 
potential. And just as we take the level of the sea 
as a zero level, and measure the heights of mountains 
above it, and the depths of mines below it, using the 
sea level as a convenient point of reference for differ- 
ences of level, so we take the potential of the earth's 
surface (for the surface oi the earth is always electrified 
to a certain degree) as zero potential^ and use it as a 
convenient point of reference from which to measure 
differences of electric potential. 

Lesson Y ,— Electrical Machines, 

38. For the purpose of procuring larger supplies oJ 
electricity than can be obtained by the rubbing of a rod 
of glass or shellac, eleotrical maoWnes havej beer 



CHAP. I.J ELECTRICITY AND MAGNETIST^L 41 

devised. All electrical machines consist of two parts, 
one for producing, the other for collecting, the electricity. 
Experience has shown that the quantities of + and ~ 
electrification developed by friction upon the two surfaces 
rubbed against one another depend on the amount of 
friction, upon the extent of the surfaces rubbed, and also 
upon the nature of the substances used. If the two 
substances employed are near together on the list of 
electrics given in Art. 5, the electrical effect of rubbing 
them together will not be so great as if two substances 
widely separated in the series are chosen. To obtain 
the highest effect, the most positive and the most 
negative of the substances convenient for the construc- 
tion of a machine should be taken, and the greatest 
available surface of them should be subjected to friction, 
the moving parts having a sufficient pressure against one 
another compatible with the required velocity. 

The earliest form of electrical machine was devised 
by Otto von Guericke of Magdeburg, and consisted of 
a globe of sulphur fixed upon a spindle, and pressed 
with the dry surface of the hands while being made to 
rotate ; with this he discovered the existence of electric 
sparks and the repulsion of similarly electrified bodies. 
Sir Isaac Newton replaced Von Guericke's globe of 
sulphur by a globe of glass. A little later the form of 
the machine was improved by various German electri- 
cians ; Von Bose added a collector or " prime con- 
ductor," in the shape of an iron tube, supported by a 
person standing on cakes of resin to insulate him, or 
suspended by silken strings ; Winckler of Leipzig sub- 
stituted a leathern cushion for the hand as a rubber ; 
and Gordon of Erfurth rendered the machine more easy 
of construction by using a glass cylinder instead of a 
glass globe. The electricity A^as led from the excited 
cylinder or globe to the prime conductor by a metallic 
chain which hung over against the globe. A pointed 
'"cllecior was not employed until after Franklin'? famou? 



42 



ELEMENTARY LESSONS ON Lchap. i. 



researches on the action of points. About 1760 De 
la Fond, Planta, Ramsden. and Cuthbertson, constructed 
machines having glass plates instead of cylinders. The 
only important modifications introduced since their time 
are the substitution of ebonite for glass, and the inven- 
tion of machines depending on the principles of induc- 
tion and convection. 

39. The Cylinder Electrical Machine. — The 
Cylinder Electrical Machine, as usually constructed, 
consists of a glass cylinder mounted on a horizontal axis 
capable of bemg turned by a handle. Against it is 
pressed from behind a cushion of leather stuffed with 
horsehair, the surface of which is covered with a 
powdered amalgam of zinc or tin. A flap of silk attached 
to the cushion passes over the cylinder, covering its 




Fig. 2::. 

upper half. In front of the cylinder stands the ^^ prime 
conductor," which is made of metal, and usually of the 
form of an elongated cylinder with hemispherical ends, 
mounted upon a glass stand. At the end of the prime 
conductor nearest the cylinder is fixed a rod bearing a 
row of fine metallic spikes, resembling in form a rake ; 
the other end usually carries a rod terminated in a brass 



CHAP. I.J ELECTRICITY AND MAGNETISM. 43 

ball or knob. The general aspect of the machine is 
shown in Fig. 23. When the handle is turned the 
friction between the glass and the amalgam- coated 
surface of the rubber produces a copious electrical 
action, electricity appearing as a + charge on the glass, 
leaving the rubber with a — charge. The prime con- 
ductor collects this charge by the following process : — 
The 4- charge being carried round on the glass acts 
inductively on the long insulated conductor, repelling a 
H- charge to the far end ; leaving the nearer end — ly 
charged. The effect of the row of points is to drive off 
in a continuous discharge - ly electrified air towards the 
attracting 4- charge upon the glass, which is neutralised 
thereby ; the glass thus arriving at the rubber in a 
neutral condition ready to be again excited. This action 
of the points is sometimes described, though less cor- 
rectly, by saying that the points collect the + electricityi 
from the glass. If it is desired to collect also the - 
charge of the rubber, the cushion must be supported on 
an insulating stem and provided at "the back with a 
metallic knob. This device, permitting either kind of 
charge to be used at will, is due to Nairne. It is, how- 
ever, more usual to use only the + charge, and to 
connect the rubber by a chain to " earth," so allowing 
the — charge to be neutralised. 

40. The Plate Electrical Machine. — The Plate 
Machine, as its name implies, is constructed with a 
circular plate of glass or of ebonite, and is usually pro- 
vided with two pairs of rubbers formed of double 
cushions, pressing the plate between them, placed at its 
highest and lowest point, and provided with silk flaps, 
each extending over a quadrant of the circle. The prime 
conductor is either double or curved round to meet the 
plate at the two ends of its horizontal diameter, and is 
ifumished with two sets of spikes, for the same purpose 
as the row of points in the cylinder machine. A 
common form of plate machine is shown in Fig. 24. 



44 



ELEMENTARY LESSONS ON [chap. i. 



Th-e action of the macliine is, in all points of theoretical 
interest, the same as that of the cylinder machine. Its 
advantages are that a large glass plate is more easy to 
construct than a large glass cylinder of perfect form, and 
that the length along the surface of the glass between the 
collecting row of points and the edge of the rubber 

cushions is greater 
in the plate than in 
the cylinder for the 
same amount of sur- 
face exposed to fric- 
tion ; for, be it re- 
marked, when the 
two electricities thus 
separated have col- 
lected to a certain 
extent, a discharge 
will take place along 
this surface, the 
length of which limits 
therefore the power 
of the machine. In 
a more modern form. 




Fig. 24, 



due to Le Roy, and modified by Winter, there is but one 
rubber and flap, occupying a little over a quadrant of the 
plate, and one collector or double row of points. ^ In 
Winter's machine the prime conductor consists of a ring- 
shaped body, for which the advantage is claimed of 
collecting larger quantities of electricity than the more 
usual sausage -shaped conductor. Whatever advantage 
the form may have is probably due to the curvature oi 
its surface being on the whole greater than that of the 
commoner form. 

41. Electrical Amalgam.— Canton, findnig glass 
to be highly electrified when dipped into dry mercury, 
suggested the employment of an amalgam of tin with 
mercury as a suitable substance wherewith to cover the 



CHAP. I.] ELECTRICITY AND MAGNETISM. 45 

surface of the rubbers. An amalgam of zinc is also 
effective ; thqugh still better is Kienmayer^s amalgam, 
consisting of equal parts of tin and zinc, mixed while 
molten with twice their weight of mercury. Bisulphide 
of tin (" mosaic gold ") may also be used. These 
amalgams are applied to the cushions with a little stiff 
grease. They serve the double purpose of conducting 
away the negative charge separated upon the rubber 
during the action of the machine, and of affording as a 
rubber a substance which is more powerfully negative 
(see list in Art. 5) than the leather or the silk of the 
cushion itself. Powdered graphite is also good. 

42. Precautions in using Electrical Machines. 
— Several precautions must be observed in the use of 
electrical machines. Damp and dust must be scrupu- 
lously avoided. The surface of glass is hygroscopic, 
hence, except in the driest climates, it is necessary to 
warm the glass surfaces and rubbers to dissipate the 
film of moisture which collects. Glass stems for in- 
sulation may be varnished with a thin coat of shellac 
varnish, or with paraffin (solid). A few drops of 
anhydrous paraffin (obtained by dropping a lump of 
sodium into a bottle of paraffin oil), applied with a bit of 
flannel to the previously warmed surfaces, hinders the 
deposit of moisture. An electrical machine which has 
not been used for some months will require a fresh coat 
of amalgam on its rubbers. These should be cleaned 
and warmed, a thin uniform layer of tallow or other stiff 
grease is spread upon them, and the amalgam, previously 
reduced to a fine powder, is sifted over* the surface. 

All points should be avoided in apparatus for 
frictional electricity except where they are desired, like 
the " collecting " spikes on the prime conductor, to let off 
a charge of electricity. All the rods, etc., in frictional 
apparatus are therefore made with knobs, so as to avoid 
5harp edges and points. 

43. Experiments with the Electrical Machine. 



46 



ELEMENTARY LESSONS ON [chap. i. 




— With the abundant supply of electricity afforded by 
the electrical machine, many pleasing and instructive 
experiments are possible. The phenomena of attrac- 

tt07t a7id reptdsion can be 
shown upon a large scale. 
Fig. 25 represents a device 
known as the electric 
chimes,^ in which two small 
brass balls hung by silk strings 
are set in motion and strike 
against the bells between 
which they are hung. The 
two outer bells are hung by 
metallic wires or chains to 
the knob of the machine. 
The third bell is hung by a 
silk thread, but communi- 
cates with the ground by a 
brass chain. The balls are 
first attracted to the electrified outer bells, then repelled, 
and, having discharged themselves against the uninsul- 
ated central bell, are again attracted, and so vibrate to 
and fro. 

By another arrangement small figures or dolls cut out 
of pith can be made to dance up and down between a 
metal plate hung horizontally from the knob of the 
machine, and another flat plate an inch or two lower and 
communicating with " earth." 

The effect of points in discharging electricity from 
the surface of a conductor may be readily proved by 
numerous experiments. If the machine be in good 
working order, and capable of giving, say, sparks four 
inches long when the knuckle is presented to the knob, 
it will be found that, on fastening a fine pointed needle 

1 Invented in 1752 by Franklin, for the purpose of warning him of the 
presence of atmospheric electricity, drawn from the air above his house by n 
pointed iron rodt 



Fig. 25. 



CHAP. I.] ELECTRICITY AND MAGNETISM. 



4J 



to the conductor, it discharges the electricit>' so effect- 
ually at its pomt that only the shortest sparks can be 




Fig. 26. 

drawn at the knob, while a fine jet or brush of pale 
blue light will appear at the point. If a lighted taper 
be held in front of the point, 
the flame will be visibly blo^^^l 
aside (Fig. 26) by the streams 
of electrified air repelled from 
the point. These air-currents 
can be felt with the hand. 
They are due to a mutual re- 
pulsion between the electrified 
air-particles near the point and 
the electricity collected on the 
point itself. That this mutual 
reaction exists is proved by 
the electric fly or electric 
reaction - mill of H amilton 
(Fig. 27), which consists of 




Fig. 27. 



a light cross of brass or straw, suspended on a pivot. 



48 ELEMENTARY LESSONS ON [chap. i. 

and having the pointed ends bent round at right 
angles. When placed on the prime conductor of the 
machine, or joined to it by a chain, the force of 
repulsion between the electricity of the points and that 
on the air immediately in front of them drives the 
mill round m the direction opposite to that m which the 
points are bent. 

Another favourite way of exhibiting electric repulsion 
is by means of a doll with long hair placed on the 
machine ; the individual hairs stand on end when the 
machine is worked, being repelled from the head, and from 
one another. A paper tassel will behave similarly if 
hung to the prime conductor. The most striking way 
of showing this phenomenon is to place a person upon 
a glass -legged stool, making him touch the knob of 
the machine ; when the machine is worked, his hair, 
if dry, will stand on end. Sparks will pass freely 
between a person thus electrified and one standing 
upon the ground. 

The sparks from the machine may be made to kindle 
spirits of wine or ether, placed in a metallic spoon, 
connected by a wire, with the nearest metallic conductor 
that runs into the ground. A gas jet may be lit h^ 
passing a spark to the burner from the finger of the per- 
son standing, as just described, upon an insulating stool. 

44. Armstrong's Hydro-Electrical Machine. — 
The friction of a jet of steam issuing from a boiler, 
through a wooden nozzle, generates electricity. In 
reality it is the particles of condensed water in the jet 
which are directly concerned. Sir W. Armstrong, who 
investigated this source of electricity, constructed a 
powerful apparatus, known as the hydro -electrical 
machine (Fig. 28), capable of producing enormous 
quantities of electricity, and yielding sparks five or six 
feet long. The collector consisted of a row of spikes, 
placed in the path of the steam jets issuing from the 
nozzles, and was supported, together with a brass ball 



CHAP. I.] ELECTRICITY AND MAGNETISM. 



40 



which served as prime-conductor, upon a glass pillar. 
The nozzles were made of wood, perforated with a 
crooked passage in order to increase the friction of 
the jet against the sides. 




Fig. 28. 

45. Convection -Induction Machines. — There is another 
class of electrical machine, differing entirely from those we have 
been describing, and depending upon the employment of a small 
initial charge which, acting inductively^ produces other charges, 
which are then conveyed by the moving parts of the machine to 
some other point where they can increase the initial charge, or 
furnish a supply of electricity to a suitable collector. Of such 
instruments the oldest is the Electrophorus of Volta, explained 
fully in Lesson III. Bennet, Nicholson, Darwin, and others, 

£ 



50 ELEMENTARY LESSONS ON [chap. i. 

devised pieces of apparatus for accomplishing by mechanism that 
.which the electrophorus accomplishes by hand. Nicholson's 
'revolving doubler consists of a revolving apparatus, in which 
an insulated caiTier can be brought into the presence of an 
electrified body, there touched for an instant to remove its 
repelled electricity, then carried forward with its acquired charge 
towards another body, to which it impatts itS-charge, and which 
ir\ turn acts inductively on it, giving it an opposite charge which 
it can convey to the first body, thus increasing its initial charge 
at every rotation. Similar instruments have been contrived by 
\'arley, Sir W, Thomson (the '* replenisher"), Topler, Carre, 
and Holtz. The two latter are perfectly continuous in their 
action, and have been well described z&. continuous electrophori. 
The machine of Holtz has come into such general use as to 
deserve explanation. 

46. Hbltz's Influence Machine. — ^The action of this machine 
is not altogether easy to grasp, though in reality simple enough 
when carefully explained. The machine m its latest form 
consists (see Fig. 29) of two plates, one. A, fixed by its edges , 
the other, B, mounted on an axis, and requiring to be rotated 
at a high speed by a band and driving pulley. There are two 
holes or windows, P ancT P , cut at opposite points of the fixed 
plate. Two pieces varnished paper, /and/*, are fastened to the 
plate above the window on the left and below the one on the 
right. These pieces of paper or armatures are upon the side of 
the fixed plate away from the movable disc, or, as we may say, 
upon the back of the plate. They are provided with narrow 
tongues which project forward through the windows towards the 
movable disc, which they nearly touch with their protruding 
points. The disc must rotate in the opposite direction to that 
in which these tongues point. Oh the front side of the moving 
disc, and opposite the forward edges of the two armatures, 
stands an oblique metal conductor, D, which need not be 
insulated. It has metal cojnbs or. spikes projecting towards the 
disc. On the right and left, supported on insulating holders, 
are two horizontal metal combs, joined to two metal rods 
terminated with brass balls, ni^ «, which in this form of machine 
merely constitute a discharging apparatus and are not concerned 
in the action of the machine. In some forms of Holtz machine 
there is no diagonal conductor D ; and as the discharging 
apparatus has then to serve both functions, the balls w, //, must 
in these forms of machine touch one another before the machine 



CHAP. L] ELECTRICITY AND MAGNETISM. 



51 




will charge itself. To work the machine a small initial charge 
must be given by an electrophoms, or by a rubbed glass rod, to 
one of the two armatures. The disc is then rapidly rotated ; 

and it is found that 
after a few turns 
the exertion required 
to keep up the ro- 
tation increases- 
greatly : at the same 
moment pale blue 
brushes of light are 
seen to issue fiom 
the points, and, on 
separating the brass 
balls, a torrent of 
brilliant sparks darts 
across the interven- 
ing space. The 
,^^^ action of the machine 

Fig. 29. ^^^^ jg ^g follows. Sup- 

pose a small + charge to be imparted at the outset to the right 
armature /' ; this charge acts inductively acro^ the intervening 
glass and air upon the comb at the lower end of the diagonal 
conductor D, repels electricity through D, leaving the lower 
points negatively electrified. These discharge negatively- 
electrified air upon the front surface of the movable disc, while 
the repelled + charge passes up along D, and is discharged 
through the upper comb upon the front face of the movable 
disc. Here it acts inductively upon the paper armrature f^ 
causing that part which is opposite the comb to be negatively 
charged, and repelling a + churge into its farthest part, viz, into' 
the tongue, which slowly discharges a + charge upon the back- 
oF the moving disc. If now the disc be turned round, this + 
charge on the back comes over, in the direction indicated by the 
arrow, from the left to the right side 5 and, when it gets opposite 
::he right tongue, is discharged into the armature/', increasing 
its charge, and thereby helps that armature to act still more 
strongly than before. Meantime the - charge, which we saw 
had been induced in the left armature/ has in tttrn reacted on 
the upper comb, causing it to emit more powerfully than before* 
a 4- charge from its points, and drawing electricity through the 
diagonal rod. The combs at the two ends of this rod therefora 



52 ELEMENTARY LESSOT^S ON [chap. i. 



both emit electrified streams of air, the upper one charging the 
upper portion of the front of the rotating disc positively, the 
lower one charging the lower portion of the disc negatively. 
The back of the rotating disc is at the same time similarly 
charged ; and the charges carried round on the back surface 
serve to increase the charges on the two armatures. Hence a 
very small initial charge is speedily raised to a maximum, the 




Fig. 29a. 

limit being reached when the electrification of the armatures Is 
so great that the leakage of electricity at their surface equals 
the gain by induction and convection. The charges let off by 
the spikes of the diagonal conductor upon the front surface of 
the. moving disc are carried round and discharged into the right 
and left conductors of the discharging apparatus, by means of 
the horizontal combs which collect the charges exactly as ex* 
plained on p. 43, Two small Leyden jars are usually added 
to increase the density of the sparks that pass between vt and n^ 



CHAP. I.] ELECTRICITY AND MAGNETISM. 53 

In some recent Holtz machines, a number of rotating discs 
fixed upon one common axis are employed, and' the whole is 
enclosed in a glass case to prevent access of damp. A small 
disc of ebonite is now usually fixed to the axis, and provided 
v/ith a rubber in order to keep up the initial charge. Iloltz has 
lately constructed a machine with thirty-two plates, 

Mascart has shown the interesting fact that the HoJtz machine is reversible 
ia its action; that is to say, that if a continuous supply of the two electricities 
(riiraished by another machine) be communicated to the armatures, the 
movable plate will be thereby set in rotation, a'nd will turn in an opposite 



Ril^hi has shown that a Holtz machine can ^neld a continuous current like 
a voltaic battery, the strength of the current being nearly proportional to 
the velocity of rotation. It was found that the electromotive force of a machine 
vyas equal to that of 52,000 Daniell's cells, or nearly 53,000 volts, at all speed: 
llie resistance, when the machine made 120 revolutions per minute, was 
2180 niillion obins ; but cnly 646 millloa ohms when making 450 revolutions 
per miuute. 

Voss has lately constructed a simple machine very like Fig. 29, but on 
Topler's plan, having small metallic buttons affixed to tlie froiit of the rotating 
piste, these buttons being lightly touched, while rotating, by small metal 
brushes fixed upon the combs, thus providing by friction a minute initial 
charge. In this machine there are no windows, but small metal arms attached 
to the paper armatures and furnished with small brushes of metal foil are 
brought roimd to the front of the rotating plate, and touch the buttons as they 
pass. The buttons therefore act as carriers of charges that are induced in 
them bj' their being touched whilst under inductive influence. 

46 {his\ WimshursVs Influence Machine. — Still more 
recent is the machine of Wimshurst (Fig. 29a) in which the 
two plates rotate in opposite directions. Each plate has a 
series of small slips of thin metal foil upon it, which serve both 
as carriers and as armatures. There are two uninsulated 
diagonal conductors at the front and back ; and two insulated 
collecting combs at the right and left, connected with a 
discharging apparatus. Each little carrier is touched by an 
uninsulated brush as it passes opposite the charged carrier of 
the other disc, and each thereby has a charge induced in it 
which it cariies over to the collecting comb on the right or left. 

Lesson VI. — The Leydeti Jar and other condenseis, 

47. It was shov/n in previous lessons that the opposite 
charges of electricity attract one another ; that electricity 
cannot flow through glass ; and that yet electricity can 
act across glass by induction. Two suspended pith- 
balls, one electrified positively and the other negatively, 
will attract one another across the intervening air. If 
a plate of glass be put between them they will still 



54 ELEMENTARY LESSONS ON [chap. i. 

attract one another, though neither they themselves nor 
the electric charges on them can pass through the glass. 
If a pith-ball electrified with a — charge be hung inside a 
dry glass bottle, and a rubbed glass rod be held outside, 
the pith-ball will rush to the side of the bottle nearest to 
the glass rod, being attracted by the + charge thus 
brought near it. If a pane of glass be taken, and a piece 
of tinfoil be stuck upon the middle of each face of the 
pane, and one piece of tinfoil be charged positively, 
and the other negatively, the two charges will attract 
one another across the glass, and v/ill no longer be found 
to be free. If the pane is set up on edge, so that neither 
piece of tinfoil touches the table, it will be found that 
hardly any electricity can be got by merely touching either 
of the foils, for the charges are " bound," so to speak, 
by each other's attractions ; each charge is inducing the 
other. In fact it v/ill be found that these two pieces of 
tinfoil may be, in this manner, charged a gieat deal 
more strongly than either of them could possibly be 
if it were stuck to a piece of glass alone, and then elec- 
trified. In other words, the capacity of a conductor is 
greatly increased ivhen it is placed near to a conduct o) 
elecirijied zvith the opposite ki^id of charge. If its 
capacity is increased, a greater quantity of electricity 
may be put into it. before it is charged to a high degiec 
of potential. Hence, such an arrangement for holding 
a large quantity of electricity may be called a con- 
denser or accumulator of electricity. 

48. Condensers.— -Next, suppose that w€ have t\\o 
brass discs, A and B (Fig. 30), set upon insulating 
stems, and that a glass plate is placed between them. 
Let B be connected by a wire to the knob of an electrical 
machine, and let A be joined by a wire to '* earth." The 
-F charge upon B will act inductively across the glass 
plate on A, and will repel electricity into the eaith, 
leaving the nearest face of A negatively electiified. 
This - charge on A wil) attract the + charge oi 



CHAP. I.] ELECTRICITY AND MAGNETISM. 



55 



B to the side nearest the glass, and a fresh supply of 
electricity will come from the machine. Thus this ar- 
rangement will become an accumulator or condenser. 
If the two brass discs are pushed up close to the glass 
plate there will be a still stronger attraction between the 
+ and - charges, because they are now nearer one 
another, and the inductive action will be greater ; hence 
a still larger quantity can be accumulated in the plates. 
We see then that the capacity of an accumulator is 
increased by bringing the plates near together. If 
now, while the discs are strongly charged, the wires 
are removed and the discs are drawn backv/ards 
the two charges will not hold 
so strongly, and there will be more 





from one another, 
one another bound 
free electrification 
than before over 
their surfaces. This 
would be rendered 
evident to the ex- 
perimenter by the 
little pith-ball elec- 
troscopes fixed to 
them (seethe Fig.), 
which would fly out Fjg, .q. 

as the brass discs 

were moved apart. We have put no further charge on 
the disc B, and )et, from the indications of the electroscope, 
we should conclude that by moving it away from disc A 
it has become electrified to a higher degree. The fact is, 
that while the conductor B was near the — charge of A 
the capacity of B was greatly increased, but on moving 
it away from A its capacity has diminished, and hence 
the same quantity of electricity now electrifies it to a 
h'gher degree than before. The presence, therefore, of 
an earth -connected plate near an insulated conductor 
increases its capacity, and permits it to accumulate a 
greater charge by attracting and condensing the elec- 



S6 ELEMENTARY LESSONS ON [chap. f. 

tricity upon the face nearest the earth-plate, the surface- 
density on this face being therefore very great. Such 
an arrangement is sometimes called a condenser, some- 
times an accumulator. We shall call such an arrange- 
ment a condenser when the object of the earth-connected 
plate is to increase the surface-density of the charge 
upon one face of the insulated conductor. The term 
accumulator is now more often applied to batteries for 
storing the energy of electric currents (Art. 415). 

The stratum of air between the two discs will suffice 
to insulate the two charges one from the other. The 
brass discs thus separated by a stratum of air constitute 
an air-condenser. Such condensers were first devised 
by Wilke and Aepinus. 

49. Dielectrics. — In these experiments the sheet of 
glass or layer of air plays an important part by permitting 
the inductive electric influences to act across or through 
them. On account of *this property these substances 
were termed by Faraday dielectrics. All dielectrics 
are insulators, but equally good insulators are not neces- 
sarily equally good dielectrics. Air and glass are far better 
insulators than ebonite or paraffin in the sense of being 
much worse conductors. But induction takes place better 
across a slab of glass than across a slab of ebonite or 
paraffin of equal thickness, and better still across these 
than across a layer of air. In other words, glass is a 
better dielectric than ebonite, or paraffin, or air. 
Those substances which are good dielectrics are said to 
possess a high inductive capacity, 

50. Capacity of a Condenser. — It appears, 
therefore, that the capacity of a condenser will depend 
upon — 

(i) The size and form of the metal plates or coatings. 

(2) The'^thinness of the stratum of dielectric between 

them ; and 

(3) The inductive capacity of the dielectric. 

51. The Leyden Jar. — The Leyden Jar, called after 



CHAP. I.] ELECTRICITY AND MAGNETISM. 




Fig. 31 



the city where it was invented, is a convenient form of 
condenser. It usually consists (Fig. 31) of a glass jar^ 
coated up lo a certain height on the inside and outside 
v/ith tinfoil. A brass knob 
fixed on the end of a stout 
brass wire passes dowjiward 
through a lid or top of dry 
ivell - varnished wood, and 
communicates by a loose bit 
of brass chain with the inner 
coating of foil. To charge 
the jar the knob is held to 
the prime conductor of an 
electrical machine, the outer 
coating being either held in 
the hand or connc^^ted to ** earth '' by a wire or chain. 
When a + charge of electricity is imparted thus to the 
inner coating, it acts inductively on the outer coating, 
attracting a ~ charge Into the face of the outer coating 
nearest the glass, and rej^elling a + charge to the outside 
of the outer coating, and (hence through the hand or wire 
to earth. After a few moments (he 
jar will have acquired its full charge, 
the outer coating being - and the 
inner +. If the jar is of good glasSj 
and diy, and free from dust, it will 
retain its charge for many hours or 
da^^s. But if a path be provided by 
which the two mutually attracting 
electricities can fiow to one another, 
they will do so, and the jar will be 
instantaneously discharged. If the 
outer coating be grasped with one 
hand, and the knuckle of the other 
hand be presented to the knob of the jar, a bright 
spark will pass between the knob and the knuckle 
with a sharp report, and at the same moment a convulsive 




Fig. 32. 



58 ELEMENTARY LESSONS ON [chap., I. 

** shock " will be commumcated to the muscles of the 
wrists, elbows, and shoulders. A safer means of dis. 
charging the jar is afforded by the dischar^ng tonga 
or discharger (Fig, 32), which consists of a jointed 
brass rod provided with brass knobs and a glass handle. 
One knob is laid against the outer coating, the other is 
then brought near the knob of the jar, and a bright 
snapping spark leaping from knob to knob announces 
that the two accumulated charges have flowed together, 
completing the discharge. 

52. Discovery of the Ley den Jar. — The dis- 
covery of the Leyden jar arose from the attempt of 
Musschenbroek and his pupil Cuneus^ to collect the 
supposed electric " fluid " in a bottle half filled with 
water, which was held in the hand and was provided 
with a nail to lead the '* fluid " down through the cork 
to the water from the electric machine.. Here the 
water served as an inner coating and the hand as an 
outer coating to the jar. Cuneus on touching the nail 
received a shock. This accidental discovery created 
the greatest excitement in Europe and America^ 

63. Residual Charges. — If a Leyden jar be 
charged and discharged and then left for a little time to 
itself, it will be found on agam discharging that a smaU 
second spark can be obtained. There is in fact a 
residual charge which seems to have soaked into the 
glass or been absorbed The return ot the residual 
charge is hastened by tapping the jar. The amount of 
the residual charge varies with the time that the jar has 
been left charged ; it also depends on the kind of the glass 
of which the jar is made. There is no residual charge 
discoverable in an air-condenser after it has once been 
discharged. 

54. Batteries of Leyden Jars. — A large Leyden 
jar will give a more powerful shock than a small one, 

> The honour of the mvenUon gf the Jar Is also claimed for Kleisi^ 
bishop of FQmeran!a« 



CHAP. 1.J ELECTRICITY AND MAGNETISlNr. 



59 



for a larger charge can be put into it : its capacity is 
greater. A Leyden jar made of tJiin glabs has a 
greater capacity as an accumulator than a thick one of 
the same size ; but if it is too thin it will be destroyed 
when powerfully charged by a spark actually piercing 
the^glass. " Toughened " glass is less easily pierced 
than ordinary glass, and hence Leyden jars made 




Fig. 33. 

of it may be made thinner, and so will hold a greater 
charge. 

If, however, it is desired to accumulate a very great 
charge of electricity, a number of jars must be em- 
ployed, all their inner coatings being connected together, 
and all their outer coatings being united. This arrange- 
ment is called a Battery of Leyden jars, or Leyden 



«Q 



ELEMENTARY LESSONS ON [chap. i. 



55. Seat of 



battery; Fig. 3^. As it has a large capacity it will 
require a large quantity of electricity to charge it fully. 
When charged it produces very powerful effectSL; its 
spark will pierce glass readily, and every care must be 
taken to avoid a shock from it passing through the 
person, as it might be fataL The " Universal Dis- 
charger " as employed with the Leyden battery is shown 
in the figure. 

the charge. — Benjamin Franklin 
discovered that the charges of the 
Leyden jar really resided on the 
surface of the glass, not on the 
metallic coatings. This he proved 
by means of a jar whose coatings 
could be removed, Fig. 34. The 
jar was charged and placed upon 
an insulating stand. The inner 
coating was then lifted out, and the 
glass jar was then taken out of the 
outer coating. Neither coating 
was found to be electrified to any 
extent,* but on agam putting the jar 
together it was found to be highly 
charge.d. The charges had all the 
time remained upon the inner and 
outer surfaces of the glass dielectric. 
^__ 50, Dielectric Strain.— Fara- 
day proved that the medium across 
which induction takes place really 
plays* an important part in the 
phenomena. It is now known 
all dieletrics across which inductive actfons are at 
are thereby strained} Inasmuch as a good 




.J^»g- 34- 



that 

work 

vacuum is a good dielectric, it is clear that it is not 



1 In the exact sciences a sirahi means an alteration or form or volume 
due to the application of a stress. A stress is the force, pressure, or other 
agency which produces a strain. 



CHAP, i.l ELECTRICITY AND- MAGNETISM. 6l 

necessarily the material particles of the dielectric sub- 
stance that are thus affected ; hence it is believed that 
electrical phenomena are due to stresses and strains in 
the so- called *' aether," the thin medium pervading all 
matter and all space, whose highly elastic constitution 
enables it to convey to us the vibrations of light though 
it is millions of times less dense than the air. As the 
particles of bodies are intimately surrounded by <' aether," 
the strains of the "aether" are also communicated to 
the particles of bodies, and they too suffer a strain. 
The glass between the two coatings of tinfoil in the 
Leyden jar is actually strained or squeezed between the 
attracting charges of electricity. When an insulated 
charged ball is hung up in a room an equal amount of 
the opposite kind of electricity is attracted to the inside 
of the walls, and the air between the ball and the walls 
is strained (electrically) like the glass of the Leyden 
jar. If a Leyden jar is made of thin glass it may give 
way tmder the stress ; and when a Leyden jar is dis- 
charged the layer of air between the knob of the jar and 
the knob of the discharging tongs is more and more 
strained as they are approached towards one another, 
till at last .the stress becomes too great, and the layer of 
air gives way, and is '* perforated " by the spark that 
discharges itself across. The existence of such stresses 
enables us to understand the residual charge of Leyden 
jars in which the glass does not recover itself all at once, 
by reason of its viscosity, from the strain to which- it 
has been subjected. This hypothesis, that electric 
force acts across space in consequence of the 
transmission of stresses and strains in the 
medinm "with ^which space is filled, is now entirely 
superseding the old theory of action-at-a-distance, which 
was logically unthinkable, and which, moreover, failed to 
account for the facts of observation. 



62 ELEMENTARY LESSONS ON [c^hap. \ 



Lesson VI L — 0^/ier Sources of Eleciricily. 

57. It was remarked at the close of Lesson I. 
(p. id), that friction was by no means the only source 
of electricity. Some of the other sources will now be 
named. 

58. Percussion. — A violent blow struck by one 
substance upon another produces opposite electrical 
states on the two surfaces. It is possible indeed to 
draw up a list resembling that of Art. 5, in such an 
order -that each substance will take a + charge on being 
struck with one lower on the list. Erman, who drew up 
such a list for a number of metals, remarked that the 
order was the same as that of the thermo-electric series 
given in Article 381, 

69. Vibration. — Volpicelli showed that vibrations 
set up within a rod of metal coated with sulphur or 
other insulating substance, produced a separation oi 
electricities at the surface separating the metal from the 
non-conductor. 

60. Disruption and Cleavage. — If a card be torn 
asunder in the dark, sparks are seen, and the separated 
portions, when tested with an electroscope, wiJl be found 
to be electrical. The linen faced with paper used in 
making strong envelopes and for paper collars, shows 
this very well. Lumps of sugar, crunched in the dark 
between the teeth, exhibit pale flashes of light. The 
sudden cleavage of a sheet of mica also produces sparks, 
and both lamin:^ are found to be electrified. 

61. Crystallisation and Solidification. — Many 
substances, after passing from the liquid to the solid state, 
exhibit electrical conditions. Sulphur fused in a glass 
dish and allowed to cool is violently electrified, as may 
be seen by lifting out the crystalline mass jvith a glass rod. 
Chocolate also becomes electrical during solidification. 
When arsenic acid co'stallisc;? out horn its solution in 



CHAP. L] ELECTRICITY AI^D MAGNETISM. 63 

hydrochloric acid, the formation of each crystal is accom- 
panfed by a flash of light, doubtless due to an electrical 
discharge, A curious case occurs when the sulphate of 
copper and potassium is fused in a crucible. It solidi- 
fies without becoming electrical, but on cooling a little 
further the crystalline mass begins to fly to powder with 
an instant evolution of electricity, 

62. Combustion. — Volta showed that combustion 
generated electricity. A piece of burning charcoal, or a 
burning pastille, such as is used for fumigation, placed in 
connection with the knob of a gold-leaf electroscope, will 
cause the leaves to diverge^ 

63. Evaporation. — The evaporation of liquids 
IS often accompanied by electrification, the liquid and 
the vapour assuming opposite states. A few drops of a 
solution of sulphate of copper thrown into a hot plati- 
num crucible produce violent electrification as they 
evaporate, 

64. Atmospheric Electricity, — Closely connected 
with the electricity of evaporation is the atmospheric 
electricity always present in the air, and due, in part 
at least, to evaporation going on over the oceans* The 
subject of atmospheric electricity is treated of sepa* 
rately in Lesson XXIV, 

65. Pressure. — A large number of substances when 
compressed exhibit electrification on their surface. Thus 
cork becomes + when pressed against amber, gutta* 
percha, and metals; while it takes a — charge when 
pressed against spars and animal substances. Abbe 
Haiiy found that a crystal of calcspar pressed between 
the dry fingers, so as to compress it along the blunt 
edges of the crystal, became electrical, and that it re- 
tained its electricity for some days. He even proposed 
to employ a squeezed suspended crystal as an electro- 
scope* A similar property is alleged of mica, topaz, 
and fluorspar^ Pressure also produces opposite kinds of 
electrification at opposite ends of a crystal of tourmaline 



64 ELEMENTARY LESSONS ON [chap. i. 

ahd of other crystals mentioned in the next para« 
graph. 

66. Pyro-elsotricity. — There are certain crystals 
which, while being heated or cooled, exhibit electrical 
charges at certain regions or poles. Cr^^stals thus 
electrified by heating or cooling are said to be P3n:o- 
electric. Chief of these is the Tourmaline, whose 
power of attracting light bodies to its ends after being 
heated has been known for some centuries. It is alluded 
to by Theophrastus and Pliny under the name of Lapis 
Lyjtacriiis. The tourmaline is a hard mineral, semi- 
transparent when cut into thin slices, and of a dark 
green or brown colour, but looking perfectly black and 
opaque in its natural condition, and possessing the power 
of polarising light. It is usually found in slightly irregu- 
lar three-sided prisms which, when perfect, are pointed 
at both ends. It belongs to the " hexagonal " system 
of crystals, but is only hemihedral, that is to say, has 
the alternate fac6s only developed. Its form is given 
inFig. 3'5, where a general view is first shown, the two 
ends A and B being depicted in separate plans. It will 
be noticed that these two ends are slightly different 
from each other. Each is made up of three sloping 
faces terminating in a points But at A the edges 
between these faces run down to tlie corners of the 
prism,, while in B the edges between the terminal faces 
run down to the middle points of the long faces of the 
prism. The end A is known as the analogous pole, 
and B as the antilogous pole. While the crystal is 
rising in temperature A exhibits + electrification, B — ; 
but if, after having .been heated, it is allowed to cool, 
the polarity is reversed ; for during the time that the 
temperature is falling B is + and A is -. If the 
temperature is steady .no such electrical effects are 
observed either at high or low temperatures; and the 
phenomena cease if the crystal be warmed above 150"* 
C. This is- not. however, due, as Gaugain declared, to 



CHAP. I.] ELECTRICITY AND MAGNETISM. 



65 



the crystal becoming a conductor at that temperature ; 
for its resistance at even higher temperatures is still so 
great as to make it practically a non-conductor. A 
heated crj'stal of tourmaline suspended by a silk fibre 
may be attracted and repelled by electrified bodies, or 
by a second heated tourmaline ; the two similar poles 
repelling one another, while the two poles of oi)posite 
form attract one another. If a ciystal be broken up, 
each fragment is found to uossess also an analogous and 
an antilogous pole. 

67. Many other crystals beside the tourmaline are 
more or less pyro-electric. Amongst these are silicate of 




112 






Fig. 35. f ij. ^o. 

zinc (*' electric calamine "), boracite, cane-su-^ar, quartz, 
tartrate of potash, sulphate of quinine, and several others. 
Boracite cr^^stallises in the form shoun in Fig. ^i^^ which 
represents a cube having four alternate corners trun- 
cated. The corners not truncated beha\^ as analogous 
poles, the truncated ones as antilogous. This peculiar 
skew-S)nmmetr)'' or hemihediy is exhibited by all the 
cr}^stals enumerated above, and is doubtless due to the 
same molecular peculiarity which determines their sin- 
gular electric property, and which also, in many cases, 
determines the optical behaviour of the cr>^stal in 
polarised light. 



66 



ELEMENTARY LESSONS ON [cHAl>. 1 



68. Animal Electricity. — Several species of crea- 
tures inhabiting the water have the power of producing 
electric discharges by certain portions of their organism. 
The best known of these are the Toi'pedo^ the Gyjn- 
notus, and the Silurus^ found in the Nile and the 
Nigen The Raia Torpedo,^ or electric ray, of which 

there are three species in- 
habiting the Mediterranean 
and Atlantic, is provided with 
an electric organ on the back 
of its head, as shown in Fig. 
2iT. This organ consists of 
laminae composed of polygonal 
cells to the number of 8oo or 
loop, or more, supplied with 
four large bundles of nerve 
fibres ; the under surface of 
the fish is — , the upper + . 
In the Gymnotus electricus, 
or Surinam eel (Fig. 38), the 
electric organ goes the whole 
length of the body along both 
sides. It is able to give a 
most terrible shock, and is a 
formidable antagonist when it 
has attained its full length of 
5 or 6 feet. Humboldt gives 
a lively account of the combats 
between the electric eels and 
the wild horses, driven by the 
natives into ithe swamps in- 
habited by the Gymnotus. 
Nobili, Matteucci, and others, have shown that nerve- 

A It is a curious point that the Arabian name for the torpedo, ra-ad^ 
signifies lightning. This is perhaps not so curious as that the Electra of 
the Homeric legends should possess certain qualities that would tend to 
suggest that she is a personification of the lightning. The resemblance 
between the names ^Uctra and electron (amber) cannot be accidentaL 




J^ig. 37- 



CHAP, I.] ELECTRICITY AND MAGNETISM. 67^ 

excitations and muscular contractions of human beings 
also give rise to feeble discharges of electricity. 




Fig. 38. 

69. Electricity of Vegetables. — Buff thought he 
detected electrification produced by plant life ; the roots 
and juicy parts being negatively, and the leaves posi- 
tively, electrified. The subject has, however, been little 
investigated. 

70. Thermo-electricity. — Heat applied at the 
junction of two dissimilar metals produces a flow of 
electricity across the junction. This subject is discussed 
in Lesson XXXIV. on Thermo-electric Currents, 

71. Contact of dissimilar Metals.^^— Volta showed 
that the contact of two dissimilar metals produced 
opposite kinds of electricity on the two surfaces, one 
becoming positively, and the -other negatively, electrified. 
This he proved m several ways, one of the most con- 
clusive proofs being that afforded by his condensing 
electroscope. This consisted of a gold-leaf elec- 
troscope combined with a small condenser. A metallic 
plate formed the top of the electroscope, and on this 
was plated a second metallic plate furnished with a 
handle, and insulated from the lower one by being well 
varnished at the surface (Fig. 68). As the capacity of 
such a condenser is considerable, a very feeble source 
may supply a quantity of electricity to the condenser with- 
out materially raising its potential, or causing the gold 
leaves to diverge. But if the upper plate be lifted, the 
capacity of the lower plate diminishes enormously, and 



68 ELE]\IENTARY LESSONS ON [chap. I. 



the potential of its Ghai*|e rises as shown by the diverg- 
ence of the gold leaves. „ To prove by the condensing 
electroscope that contact of dissimilar metals does 
produce electrification, a small compound bar made of 
two dissimilar metals — ^ say zinc and copper — soldered 
together, is held in the hand, and one end of it is touched 
against the lower plate, the upper plate being placed in 
contact with the ground or touched with the finger. 
When the two opposing charges have thus collected in 
the condenser the upper plate is removed, and the 
diverging of the gold leaves shows the presence of a 
free charge, which can afterwards be examined to see 
whether it be + or - . For a long time the existence 
of this electricity of contact was denied, or rather it was 
declared to be due (when occurring in voltaic combina- 
tions such as are described in Lesson XIJI.) to chemical 
actions going on ; whereas the real truth is that the 
electricity of contact and the chemical action are both 
due to molecular conditions of the substances whidi 
come into contact with one another, though we do not 
yet know the precise nature of the molecular conditions 
which give rise to these two effects. Later experiments, 
especially those made with the . delicate elect] ometers of 
Sir W. Thomson (Fig. loi), put beyond doubt the reality 
of Volta's discovery. One simple experiment explains the 
method adopted, A thin strip or 
needle of metal is suspended so as 
to turn about a point C It is elec- 
trified from a known source. Under 
it are placed (Fig. 39) two semicir- 
cular discs, or half-rings of dissimilar 
metals. Neither attracts or repels 
^. the electrified needle until the two are 

brought into contact, or connected by 
a third piece of metal, when the needle immediately turns, 
being attracted by the one that is oppositely electrified, and 
repelled by the one that is similarly electrified with itself. 




CHAP. I.] ELECTRICITY AND MAGNETISM. 



69 



72. Volta found, moreover, that the differences of 
electric potential between the different pairs of metals 
were not all equal. Thus, while zinc and lead were 
respectively + and - to a slight degree, he found zinc 
and silver to be respectively + and - to a much greater 
degree. He was able to arrange the metals in a series 
such that each one enumerated became positively elec- 
trified when placed in contact with one^ below it in the 
series. Those in italics are added from observations 
made since Volta's time — 

Contact -Series of Metals (in Air). 

+ Sod ii tin. 

Zinc. 

Lead. 

Tin. 

Iron. 

Copper. 

Silver. 

Gold. 

Pfafj'vit77t, 
— Graphilc (Carbon). 
Though Volta gave rough approximations, the actual 
numerical values of the differences of potential for 
different pairs of metals have only lately been measured 
by Ayrton and Perry, a few of whose results are tabu- 
lated here — 

Differ ence of Poteutial 
(in volts). 

•210 
'069 

•313 
•146 

•11^ 



Zinc 1 

Lead \ 

Tin \ 

Iron ^ 

Copper J 

Platinum ) 

Carbon ! 



70 ELEMENTARY LESSONS ON [chap. i. 

The difference of potential between zinc and carbon is 
the same as that obtained by adding the successive 
differences, or 1:09 volts.^ Volta's observations may 
therefore be stated in the following generalised form, 
known as Volta's La"W. Th^ difference of potential 
between any two metals is equal to the stmt of the differ- 
ences of potentials between the i^cterveniiig inetals in the 
contact'Series. 

It is most important to notice that the order of the 
metals in the contact -series in air is almost identical 
with that of the metals arranged according to their 
electro-chemical power, as calculated from their chemical 
equivalents and their heat .of combination with oxygen 
(see Table, Art. 422 {bis). From this it would appear 
that the difference of potentials between a metal and the 
air that surrounds it measures the tendency of that 
metal to become oxidised by the air. If this is so, and 
if (as is the case) the air is a bad conductor while the 
metals are good conductors, it ought to follow that when 
two different metals touch they equalise their own 
potentials by conduction but leave the films of air that 
surround them at different potentials. AD the exact 
experiments yet made have measured the difference of 
potentials not between the metals themselves, but 
between the air near one metal and that near another 
metal. All this is most important in the theor)'- of the 
voltaic cells. Mr. James Brown has lately demonstra ed 
the existence on .freshly-cleaned metal surfaces oi flins 
of liquid or condensed gases, and has shown that 
pohshed zinc and copper when brought so near that 
their films touch will act as a battery. 

73. A difference of potential is also produced by the 
contact of iivo dissimilar liquids with one another. 

A liquid and a mefal in contact with one another 
also exhibit a difterence of potential. 

X For the dennition of the ifolt, or unit of difference of potential, see Art 

323. 



CHAP, ij ELECTRICITY AND MAGNETISM, 7? 



A hot metal placed in contact with a cold piece of 
the same metal also produces a difference of potential, 
electrical separation taking place across the surface of 
contact. 

Lastly, it has been shown Uy Prof. J. J. Thomson that 
the surface of contact between- two non-conducting sub- 
stances, such as sealing-wax and glass, is the seat of a 
permanent difference of potentials. 

74. Magneto-electricity. — Electricity, in the form 
of currents flowing along in wires, can be obtained from 
magnets by moving closed conducting circuits in their 
neighbourhood. As* this source of electricity yields 
currents rather than statical; charges of electricity, the 
account of it is. deferred to Lesson XXXVI. 

75. Summary. — We have seen in the preceding 
paragraphs how almost all conceivable agencies may 
produce electrification in bodies. The most important 
of these -are friction, heat, chemical action, magnetism, 
and the contact of dissimilar substances. We noted 
that the production of electricity by friction depended 
largely upon the molecular condition of the surfaces. 
We may here add. that the difference of potentials pro- 
duced by contact of dissimilar substances also varies 
with the temperature and with the nature of the medium 
(air, vacuum, etc.) in which ^ the experinnents are made. 
Doubtless this source also depends upon the molecular 
conditions of dissimilar substances being different ; the 
particles at the surfaces being of different sizes and 
shapes, and vibrating with different velocities and wth 
different /orces. There are (see Art. 10) good reasons 
for thinking that the electricity of friction is really due 
to electricity of contact, excited at successive portions of 
the surfaces as they are moved over one another. But 
of the molecular conditions of bodies which determine 
the production of electricity where they come into con- 
tact, little or nothing is yet knowni. 



12 ELEMENTARY LESSONS ON [chap, ii 



CHAPTER II 

MAGNETISM. 

Lesson VI I L — Magnetic Ailraclion mid Repu1sio7i 

76. Natural Magnets or Lodestones* — Tlie 
name Mag*net {/Sfirgnes Lnpls) wa^ gi\'en by the 
ancients to certain hard black siones fuund in various 
pans of the world, notably at Magnena in Asia Minor, 
which possessed the property of attracting to them small 
pieces of iron or steel. This magic property, as they 
deemed it, made the magnet-stone famous ; but it was 
not until tlie tenth or twelfth century that such stones 
were discovered to have the still more remarkable pio- 
perty of pointing noith and south when hung up by 
a thread. This property was turned to advantage in 
navigation, and from that time the magnet received the 
name of Lodestone ^ (or " leading-slone "). The 
natural magnet or lodestone is an ore of iron, known to 
mineralogists as inagnefife and having the chemical 
composition Feg O^. This ore is found in quantities in 
Sweden, Spain, Arkansas, the Isle of Elba, and other 
parts of the world, though not always in the magnetic 
condition. It frequently occurs in crystals ; the usual 
form being the regular octahedron. 

77. Artificial Magnets. — If a piece of iron, or, 
better still, a piece of hard steel, be rubbed with a lode- 
stone, it will be found to have also acquired the properties 
characteristic of the magnet; it will attract light bits of 

1 Tbe common rpelJing /^a^jfstone is duo to inisapprelieusiuii. 



CHAP. II.] ELECTRICITY AND MAGNETISM. 



n 



iron, and, if hung up by a thread it will point north 
and south. Figures 
40 and 41 I'epresent 
a natural lodestone 
and an artificial 
magnet of steel, each 
of which has been 
dipped into iron- 
filings ; the filings 
are attracted and 
adhere in tufts. 




Figs. 40 and 41.. 



78. Discoveries of Dr. Grilbert. — This was: all, or 
nearly all, tliat was known of the magnet until 1600, 
when Dr. Gilbert published a l^rge number of magnetic 
discoveries in his famous work ** De Magjtete,? He 
obserA'-ed that .the attractive power of a magnet appears 
to reside at two regions, and in a long-shaped magnet 
these regions, or poles, are usually at the ends (see Figs. 
40 and 41). The portion of the magnet which lies be- 
tween the two poles is apparently less magnetic, and 
does jiot attract iron-filings so strongly ; ami all round 
the magnet, halfway between the poles, thepe is no 
attraction at all. This region Gilbert called the equator 
of the magnet, and the imaginary line joining the pojes 
he termed the axis. 

79. Magnetic Needle. — To investigate more fully 
the magnetic forces a inag*netio needle is Employed. 
Tliis consists (Fig. 42) of a light needle cut out of steel, 
and fitted with a little cap of brass, glass, or agate, by 
means of which it can be hung upon a sharp point, so 
as to tUm ^^ith ver>' little friction. It is made into a 
raagnet by being rubbed upon a magnet ; and when 
Chus magnetised will turn into the north -and -south 
position, or, as we should say, will set itself in the 
"-magnetic meridian'' (Art. 136). The compass sold 
by opticians consists of such a needle balanced above a 
card marked with the " points of the compass.'* 



74 



ELEMENTARY LESSONS ON [chap. ii. 



80, Magrnetio Attractions and Repulsions. — 

If we take a magnet 




Fig. 42. 



(either natural or 
artificial) in our hand 
and present the two 
*' poles " of it succes- 
sively to the north- 
pointing end of a 
magnetic needle, we 
shall observe that 
one pole of the mag- 
net attracts it, while 
the other repels it. 
(Fig. 43.) If we 
repeat the experi- 
ment on the south- 
pointing end of the 
magnetic needle, we 
shall find that it is 
repelled by one pole 
and attracted by 



the other ; and that the same pole which attracts the 
north-pointing end 
of the needle re- 
pels the south- 
pointing end. 

If we try asimir 
lar experiment on 
the magnetic 

needle, using for 
a magnet a second 
magnetised needle 
which has previ- 
ously been sus- 
pended, and which has its north-pointing end marked 
•to distinguish it from the south-pointing end, we shall 
discover that the N.-pointing pole repels the N.-pointing 




Fig. 43- 



CMAP. II.] ELECTRICITY AND MAGNETISM. >5 

pole, and that the S.-pointing pole repels the S.-pointing 
pole ; but that a N.-pointing pole attracts and is attracted 
by a S.-pointing pole. 

81. Two kinds of Magnetic Poles. — There would 
therefore appear to be two opposite kinds of magnetism, 
or at any rate two opposite kinds of magnetic poles, 
which attract or repel one another ii) very much the 
same fashion as the two opposite kinds of electricity do ; 
and one of these kinds of magnetism appears to have a 
tendency to move toward the north and the other to 
move toward the south. It has been proposed to call 
these two kinds of magnetism "north-seeking magnet- 
ism " and " south-seeking magnetism," but for our pur- 
pose it is sufficient to distinguish between the two kinds 
of poles. In common parlance the poles of a magnet 
are called the " North Pole '■' and " South Pole " respect- 
ively, and it is usual for the makers of magnets to mark 
the N.-pointing pole with a letter N. It is therefore 
sometimes called the " marked " pole, to distinguish it 
from the S.-pointing or " unmarked " pole. We shall, to 
avoid any doubt,^ call that pole of a magnet which 
would, if the magnet were suspended, tend to turn to the 

1 It is necessary to be precise on this point, as there is some confusion in 
the existing text-books. The cause of the confusion is this : — If the north- 
pointing pole of a needle is attracted by magnetism residing near the North 
Pole of the earth, the law of attraction (that unlike poles attract), shows us 
that these two poles are really magnetically of opposite kinds. Which are 
we then to call north magnetism ? That which is at the N. pole of the earth? 
If so, we must say that the N.-pointing pole of the needle contains south 
magnetism. And if we call that north magnetism which points to the north, 
then we must suppose the magnetic pole at the north pole of the earth to have 
south masrnetism in it. In either case there is then a difficulty. The Chinese 
and the French call the N.-pointIng pole of the needle a south pole, and the 
S.-pomtiiig pole a north pole. Sir Wm. Thomson also calls the N. -pointing 
pole a *'True South" pole. But common practice gees the other way, and 
calls the N.-pointing pole of a magnet its '* North " pole. For experimental 
purposes it is issual to paint the two poles of a magnet of different colours, 
Ae N. -seeking pole beuig coloured red and the S. -seeking pole hliie ; but 
here again, strangely enough, authorities differ, for in the collections of 
apparatus at the Royal Institjition and Royal School of Klines, the colours 
are used in exactly the opposite way to this, which is due to Sir G. Airy < 



^6 ELEMENTARY LESSONS ON [chap. n. 

north, the " North -seeking " pole, and the other the 
" South-seeking " pole. 

We may therefore sum up our observations in the 
concise statement : Like magnetic poles repel one another; 
unlike poles attract one another. This we mav call the 
first law of magnetism. 

82. The two Poles inseparable. — It is impossible 
to obtain a magnet with only one pole. If we magnetise 
a piece of steel wire, or watch spring, by rubbing it wfth 
one pole of a magnet, we shall find that still it has two 
poles — one N.-seeking, the Ocher S. -seeking. And if we 
break it into two parts, each part will still have two 
poles of opposite kinds. 

83. Magrnetio Force. — The force with which a 
magnet attracts or repels another magnet, or any piece 
of iron or steel, we shall call magnetic force?- The 
force exerted by a magnet upon a bit of iron or on another 
magnet is not the same at all distances, the force being 
greater when the magnet is nearer, and less when the 
magnet is farther oflf. In fact the attraction due to a 
magnet-pole falls oflf inversely as the square of the 
distance from the pole. (See Art. 117.) 

V/henever a force acts thus between two bodies, it acts 
on both of them, tending to move both. A magnet will 
attract a piece of iron, and a piece of iron will attract a 
magnet. This was shown by 
Sir Isaac Newton, who fixed a 
magnet upon a piece of cork and 
floated it in a basin of water 
(Fig. 44), and found that it moved 
across the basin when a piece of 
^^^' ^^' 4ron was held near. A compass 

needle thus floated turns round and points north and 
south ; but it does not rush towards the north as a 
whole, nor towards the south. The reason of this will 
be explained later, in Art. 117. 

I See footnote on " Force," Art. 155. * 






CHAP. II.] ELECTRICITY AND MAGNETISM. 77 

Gilbert suggested that the force of a magnet might be 
measured by making it attract a piece of iron hung to 
one arm of a balance, weights being placed in the scale- 
pan hangin]^ to the other arm ; and he found, by hang- 
ing the ^ magnet to the balance and placing the iro7t 
beneath it, that the effect produced was the same. The 
action and reaction are then equal for magnetic forces, 

84. Attraction across bodies. — If a sheet of 
glass, or wood, or paper, be interposed between a magnet 
and the piece of iron or steel it is attracting, it will still 
attract it as if nothing were interposed. A magnet 
sealed up in a glass tube stiU acts as a magnet. Lucre- 
tius found a magnet put into a brass vase attracted iron 
filings through the brass. Gilbert surrounded a magnet 
by a ring of flames, and found it still to be subject to 
magnetic attraction from without. Across water, vacuum, 
and all known substances, the magnetic forces will act ; 
with the single exception, however, that magnetic force 
will not act across a screen of iron or other magnetic 
material. If a small magnet is suspended inside a 
hollow ball made of iron, no outside magnet will affect it 
A hollow shell of iron will therefore act as a magitetic 
cage^ and screen the space inside it from magnetic 
influences. 

85. Magnetic Substances. — A distinction was 
drawn by Gilbert between magnets and vtagnetic 
substances. A magnet attracts only at its poles, and 
they possess opposite properties. But a lump of iron 
will attract either pole of the magnet, no matter what 
part of the lump be presented to the magnet. It has no 
distinguishable fixed "poles," and no magnetic "equator." 
A true magnet has poles, one of which is repelled by the 
pole of another magnet. 

86. Other Magnetic Metals. — Later experimenters 
have extended the list of substances which are attracted 
by a magnet. In addition to iron (and steel) the follow^ 
ing metals are recognised as magnetic : — 



7$ ELEMENTARV LESSONS ON [chap, lu 

Nickel. ^ Chromium. 

Cobalt. Cerium. 

Manganese, 

and a few others. But only nickel and cobalt are at all 
comparable with iron and steel in magnetic power, and 
even they are ver)' far inferior. Other bodies, sundry salts 
of iron and other metals, paper, porcelain, and oxygen 
gas, are also very feebly attracted by a powerful magnet. 
&7. Diamagnetism. — A number of bodies, notably 
bismuth, antimony, phosphorus, and copper, are repelled 
from the poles of a magnet. Such bodies are called 
diamagnetic bodies; a fuller account of them will be 
found in Lesson XXVI IL 

88. The Earth a Magrnet. — The greatest of 
Gilbert's discoveries was that of the inherent magnetism 
of the earth. The earth is itself a great magnet^ 
whose " poles " coincide nearly, but not quite, with the 
geographical north and south poles, and therefore it causes 
a freely-suspended magnet to turn into a north and south 
position. The subject of 2'e7'r est rial Magnetism is 
treated of in Lesson XH. It is evident from the first 
law of magnetism that the magnetic condition of the 
northern regions of the earth must be the opposite to 
that of the north-seeking pole of a magnetised needle. 
Hence arises the difficulty alluded to on page 75. 

89. Magnetic Induction. — Magnetism may be 
communicated to a piece of iron, without actual contact 
with a magnet. If a short, thin unmagnetised bar of 
iron, be placed near some iron filings, and a magnet be 
brought near to the bar, the presence of the magnet 
will induce magnetism in the iron bar, and it will now 
attract the iron filings (Fig. 45). This inductive action 
is very similar to that observed in Lesson III. to take 
place when an electrified body was brought near a non- 
electrified one. The analogy, indeed, goes farther than 
this, for it is found that the iron bar thus magnetised by 
induction will have two poles ; the pole nearest to the 



.HAP. 11.] ELECTRICITV AND MAGNETISIM. 



79 



pole of the inducing magnet being of the opposite kind^ 
while the pole at the farther end of the bar is of the 
same kind as the inducing pole. Magnetism can, how- 
ever, only be induced in those bodies which we have 
enumerated as magnetic bodies ; and those bodies in 
which a m.agnetising force produces a high degree of 
magnetisation are said to possess a high co -efficient 
of magnetisatioji. It will be shown presently that 
magnetic induction takes place along certain direc- 
tions called lines of magnetic inductio7i^ or lines of 
viag7ietic force^ which may pass either through iron 
and other magnetic media, or through air, vacuum, 




^ig- 45- 

glass, or other non-magnetic media : and, since induction 
goes on most freely in bodies of high magnetic suscepti- 
bility, those lines of force are sometimes (though not 
too accurately) said to '' pass by preference through 
magnetic matter,'' or, that *' magnetic matter conducts 
the lines of force." 

Although magnetic induction takes place at a distance 
across an intervening layer of air, glass, or vacuum, 
there is no doubt that the intervening medium is directly 
concerned in the transmission of the magnetic force, 
though probably the true medium is the '* ^ther " of 
space surrounding the molecules of matter, not the 
molecules themygelves. 



So ELEMENTARY LESSONS ON [chap. ii. 

We now can see wJiy a magnet should attract a not- 
previously-magnetised piece of iron; it first magnetises 
it by induction and then attracts it : for the nearest end 
will have the opposite kind of magnetism induced in it, 
and will be attracted with a force exceeding that with 
which the more distant end is repelled. But induction 
precedes attraction, 

90. Retention of Magnetisation. — Not all mag- 
netic substances can become magnets permanently. 
Lodestone, steel, and nickel, retain permanently the 
greater part of the magnetism imparted to them. Cast 
nron and many impure qualities of wrought iron also 

retain magnetisrii imperfectly. 
Pure soft iron is, • however, only 
temporarily magnetic. The 

following experiment illustrates 
the matter : — Let a few .pieces 
of iron rod, or a few soft iron 
nails be taken. If one of these 
(see Fig. 46) be placed in con- 
tact with the pole of a perma- 
nent steel magnet, it is attracted 
to it, and becomes itself a tem- 
*^* ^ ' porary magnet. Another bit of 

iron may then be hung to it, and another, until a chain 
of four or five pieces is built up. But if the steel 
magnet be removed from the top of the chain, all the 
rest drop off, and are found to be no longer magnetic. 
A similar chain of steel needles may be formed, but 
they will retain their magnetism permanently. 

It will be found, however, that a steel needle is more 
difficult to magnetise than an iron needle of the same 
dimensions. It is harder to get the magnetism into 
steel than into iron, and it is harder to get the magnetism 
out of steel than out of iron ; for the steel retains the 
magnetism, once put into it. This power of resisting 
magnetisation or demagnetisation, is sometimes called 




CHAP. II.] ELECTRICITY AND MAGNETISM. 81 



coefcivB force; a much better term, due to Lament, 
is retentivity. The retentivUy of hard-tempered steel 
is greats that of soft wrought iron is very small. The 
harder the steel, the greater its retentivity. 

©L Theories of MagnetisnL — The student will 
not have failed to observe the striking analogies between 
the phenomena of attraction, repulsion, induction, etc., 
of magnetism and those of electricity. Yet the two sets 
of phenomena are quite distinct. A positively electrified 
body does not attract either the North -pointing or the 
South -pointing pole of the magnet as such ; in fact, it 
attracts either pole' quite irrespective of its magnetism, 
just as it will attract ahy other body. There does 
exist, indeed, a direct relation between magnets and 
currents of electricity, as will be later explained. There 
is none known, however, between magnets and stationary 
charges of electricity. 

No theory as to the nature of magnetism has yet 
been placed before the reader, who has thus been told 
the fundamental facts without bias. In many treatises 
it is the fashion to speak of a magnetic fluid or fluids ; 
it is, however, absolutely certain that magnetism is not 
afltdd^ whatever else it may be. The term, which is a 
relic of bygone, times, is only tolerated because, under 
certain circumstances, magnetism distributees itself in 
magnetic bodies in the same manner as an elastic 
fluid would ,do. Yet the reasons* against its being a 
fluid are even more conclusive than in the case of 
electricity. An electrified body when touched against 
another conductor, electrifies the conductor by giving 
up a part of its electricity to it. But a magnet when 
rubbed upon a piece of- steel magnetises it without 
giving up or losing any of its own magnetism. A fluid 
cannot possibly propagate itself indefinitely without loss. 
The arguments to be derived 'from the behaviour of 
a magnet on breaking, and from other experiments 
narrated in Lesson X., are even stronger. No theory 



82 ELEMENTARY LES-SONS ON [chap. «• 

of magnetism will therefore be propounded until these 
facts have been placed before the student. 



Lesson \1^.— Methods of Making Magnets. 

92. Magnetisation by Single Touch. — It has 
been so far assumed that bars or needles of steel were 
to be magnetised by simply touching them, or stroking 
them from end to end with the pole of a permanent magnet 
of lodestone or steel. In this case the last touched point 
of the bar will be a pole of opposite kind to that used 
to touch it ; and a more certain effect is produced if one 
pole of the magnet be rubbed on one end of the steel 
needle, and the other pole upon the other end. There 
are, however, better ways of magnetising a bar or needle. 

93. Magnetisation by Divided Touch. — In this 
method the bar to be magnetised is laid down hori- 
zontally ; two bar magnets are then placed down upon it, 
their opposite poles being together. They are then 
drawn asunder from the middle of the bar towards its 



^ 





a I ^ ^ I A" 

Fig. 47. 

ends, and back, several times. The bar is then turned 
over, and the operation repeated, taking care to leaver ofif 
at the middle (see Fig. 47). The process is more 
effectual if the ends of the bar are meantime supported 
on the poles of other bar magnets, the poles being of 
the same names as those of the two magnets above 
them used for stroking the steel bar. 

94. Magnetisation by Double Touch. — Another 



CHAP, II.] ELECTRICITY AND MAGNETISM. 83 

method^ known as double touchy differs slightly from 
that last described. A piece of wood or cork is inter 
posed between the ends of the two bar magnets employed, 
and they are then both moved backwards and forwards 
along the bar that is to be magnetised. By none of 
these methods, however, can a steel bar be magnetised 
beyond a certain degree of intensity. 

95. Laminated Magnets. — It is found that long 
thin steel magnets are more powerful in proportion to 
their weight than thicker ones. Hence it was proposed 
by Scoresby ^ to construct compound magnets, consisting 
of thin laminae of steel separately magnetised, and after- 
wards bound together in bundles. These laminated 
magnets are more powerful than simple bars of steel. 

96. Magnetisation derived from the Earth. — 
The magnetism of the earth may be utilised, where no 
other permanent magnet is available, to magnetise a bar 
of steel. Gilbert states that iron bars set upright for 
a long time, acquire magnetism from the earth. If a 
steel poker be held in the magnetic meridian, with the 
north end dipping down, and in this position be struck 
with a wooden mallet, it will be found to have acquired 
magnetic properties. Wires of steel subjected to torsion, 
while in the magnetic meridian, are also found to be 
thereby magnetised. 

97. Magnetisation after Heating, — Gilbert dis- 
covered also that if a bar of steel be heated to redness, 
and cooled, either slowly or suddenly, while lying in the 
magnetic meridian, it acquires magnetic polarity. No 
such property is acquired if it is cooled while lying east- 
and-west. It has been proposed to make powerful 
magnets by placing hot bars of steel to cool between the 
poles of very powerful electro-magnets ; and Carrd has 
recently produced strong magnets of iron cast in moulds 
lying in an intense magnetic field. 

1 A similar suggestion was made by Geuns of Venlo in 1768. Similar 
magnets have been constructed recently by Jamin. 



84 ELEMENTARY LESSONS ON [chap, ti 

98. Magnetisation by Ourrents of Electricity. 
A strong current of electricity carried in a spiral wire 
around a bar of iron or steel, magnetises it more power- 
fully than in any of the preceding operations. In the 
case of a soft iron bar, it is only a magnet while the 
current continues to flow. Such a combination is 
termed an Electro-mag'net ; it is fully described in 
Lesson XXVL Elias of Haarlem proposed to mag- 
netise steel bars by passing them through a \vire coiled 
up into a ring of many turns, through which a strong 
current was sent by a voltaic batteiy. Tommasi claims 
to have magnetised steel bars by passing a current of 
hot steam round them in a spiral tube : but the matter 
needs further evidence. 

99. Destruction of Magnetism. — A steel magnet 
loses its magnetism partially or wholly if subjected to 
rough usage, or if purposely hit or knocked about. It 
also loses its magnetism, as Gilbert showed, on being 
raisf^d to a red-heat. 

100. Effects of Heat on Magnetisation. — If a 
permanent steel magnet be warmed by placing it in hot 
or boiling water, its strength will be thereby lessened, 
though it recovers partially on coolings Chilling a 
magnet increases its strength. Cast iron ceases to 
be attracted by a magnet at a bright red-heat, or at a 
temperature of about 700*^ C. Cobalt retains its mag- 
netism at the highest temperatures. Chromium ceases 
to be magnetic at about 500° C, and Nickel at 350* 
C. Manganese exhibits magnetic attraction only when 
cooled to — 20** C. It has therefore been surmised that 
other metals would also become magnetic if cooled to a 
low enough temperature ; but a very severe cooling to 
100° below zero destro3's tl^e magnetism of steel magnets. 
The magnetic metals at high temperatures do not be 
come diamagnetic, but are still feebly magnetic. 

101. Forms of Magnets. — Natural Magnets are 
usually of irregular form, though they are sometimes 



CHAP. II.) ELECTRICITV AND MAGNETISM. 85 

reduced to regular shapes by cutting or grinding. 
Formerly it was the fashion 10 mount them with soft iron 
cheeks or ** armatures ** to serve as pole-pieces. 

For scientific experiments bar magnets of hardened 
steel are commonly used ; but for many purposes the 
horseshoe shape is preferred. In the horse shoe magnet 
the poles are bent round so as to approach one another, 
the advantage here being that so both poles can attract 
one piece of ircJn. The ** annature,'* or ^* keeper," as 
the piece of soft iron placed across the poles is named, is 
itself rendered a magnet by induction when placed across 
xlie poles ; hence, when both poles magnetise it, the force 
with which it is attracted to the magnet is the greater. 

102. Magnetio Satxiration.^ — A magnet to which 
as powerful a degree of magnetisation as it can attain to 
has been given is said to be ^^ saturated.'*^ Many of 
the methods of magnetisation described will excite in a 
magnet a higher degree of magnetism than it is able to 
retain permanently. A recently magnetised magnet will 
occasionally appear to be supersaturated^ even after 
the application of the magnetising force has ceased. 
Thus a horse-shoe-shaped steel magnet will support a 
greater weight immediately after being magnetised than 
it will do after its armature has been once removed from 
its poles. Even soft iron after being magnetised retains 
a small amount of magnetism when its temporary mag- 
netism has disappeared. This small remaining magnetic 
charge is spoken of as residual magnetism. 

Strength of a Magnet. — The '' strength ^^ of a 
magnet is not the same thing as its '* Iifting-power." The 
'* strength " of a magnet is the " strength " of its poles. 
The '* strength " of a magnet pole must be measured by 
the magnetic force which it exerts. Thus, suppose there 
are two magnets, A and B, whose strengths we compare 
by making them each act upon the N. pole of a third 
magnet C. If the N pole of A repels C with twice as 
much force as that with which the N. pole of B placed 



86 ELEMENTARY LESSONS ON [chap, il 

at the same distance would repel C, then we should say 
that the ** strength " of A was twice that of B. Another 
way of putting the matter is to say that the *' strength " 
of a pole is the amount of free magnetism at that pole. 
By adopting the unit of strength of magnet poles as 
defined in Art. 125, we can express the strength of ary 
pole in numbers as so many '^ units " of strength. 

103. Lifting Power. — The lifting power of a magnei 
(also called its ^^ portative force ") depends both upon 
the form of the magnet and on its magnetic strength. A 
horse-shoe magnet will lift a load three or four times as 
great as a bar magnet of the same weight will lift. The 
lifting power is greater if the area of contact between the 
poles and the armature is increased. Also the lifting 
power of a magnet grows in a very curious and unex- 
plained way by gradually increasing the load on its 
armature day by day until it bears a load which at the 
outset it could not have done. Nevertheless, if the load 
is so ir'^reased that the armature is torn off, the power 
of the magnet falls at once to its original value. The 
attraction between a powerful electro-magnet and its 
armature may amount to 200 lbs. per square inch, or 
14,000 grammes per square centimetre. Small magnets 
lift a greater load in proportion to their own weight than 
large ones.^ A good steel horse-shoe magnet weighing 
itself one pound ought to lift twenty pounds' weight. 
Sir Isaac Nev/ton is said to have possessed a little lode- 
stone mounted in a signet ring which would lift a piece 
of iron 200 times its own weight. 

1 Bernoulli gave the following rule for finding the lifting-power / cT a 
magnet whose weight was w : — 



' = alj w; 



where « is a constant depending on the goodness of the steel and the method 
of -magnetising it. In the best steel magnets made at Haarlem by V. 
Wetteren this coefficient was from 19*5 to 23. In Breguet's magnets, made 
from Allevard steel, the. value is equally high. 



CHAP. 11.] ELECTRICITY AND l\iAGKETlSxM. 8^ 

Lesson X. — Distribttiion of Magnetism. 

104. Normal Distribution. — In an ordinary bar 
magnet the poles are not quite at the ends of the bar, 
but a little way from it ; and it can be shown that this is 
a result of the way in which the magnetism is distributed 
in the bar, A very long, thin, uniformly magnetised bar 
has its poles at the ends ; but in ordinary thick magneto 
the " pole " occupies a considerable region, the " free 
magnetism " falling off gradually from the ends of the 
bar. In each region, however, a point can be deterniined 
at which the resultant magnetic forces act, and which 
may for most purposes be considered as the pole. In 
certain cases of irregular magnetisation it is possible to 
have one or more poles between . those at the ends. 
Such poles are called consequejit poles (see Fig. 51). 

105. Magnetic Field, — The space all round a 
magnet pervaded by the magnetic forces is termed the 
"yf^/^" of that magnet. It is most intense near the pole 
of the magnet, and is weaker and weaker at greater dis- 
tances away from it. At eveiy point in a magnetic field 
the force has a particular strength, and the magnetic 
induction acts in a particular direction or line. In the 
horse-shoe magnet the field is most intense between the 
two poles, and the lines of magnetic induction are ounces 
which pass from one pole to the other across the field. 
A practical v/ay of investigating the distribution of the 
lines of induction in a field is given in Art. 108, under the 
title ^' Magnetic Figures." When the armature is placed 
upon the poles of a horse-shoe magnet, the force of the 
magnet on all the external regions is weakened, for the 
induction now goeb on through the iron of the keeper, 
not through the surrounding space. In fact a closed 
system of magnets — such as that made by placing four 
bar magnets along the sides of a square, the N. pole of 
one touching the S. pole of the ne^d; — has no external 
field of force. A ring cf steel may thus be magnetised 



88 



ELEMENTARY LESSONS ON [chap. ii. 



so as to have neither external field nor poles ; or rather 
any point in it may be regarded as a N. pole and a S. 
pole, so close together that they neutralise one another's 
forces. 

That poles of opposite name do neutralise one another 
may be shown by the well-known experiment of hanging 
a small object — a steel ring or a key — to the N. pole of 
a bar magnet. If now the S. pole of another bar magnet 
be made to touch the first the two poles will neutralise 
each other's actions, and the ring or key will drop down. 

106. Breaking a Magnet. — We have already stated 
that when a magnet is broken into two or more parts, each 
is a complete magnet, possessing poles, and each is 
nearly as strongly magnetised as the original magnet. 
Fig. 48 shows this. If the broken parts be closely joined 



rOiiliiilliBIIBIi^^ 



iiiiliiiiiiillhliliiliiiiiiiliilliiligliiiiii^ 



Fig. 48. 

these adjacent poles neutralise one anoiner and disappear, 
leaving only the poles at the ends -as before. ' If a magnet 
be ground to powder each fragment will still act as a 
little magnet and exhibit polarity. A magnet may there- 
fore be regarded as composed of many little magnets 



N 












s' 


tr 














s 


n 


A' 


n 


.5 


n 


^ 


n s 


n 


s 


n 


^ 


n 


s 


-h 


s 


n 


S 


n 


s 


n 


8 


n s 


n 


s 


n 


s 


n 


s 


n 


s 


ii ' 


S 


n 


,<? 


n 


S 


n s 


n 


s 


n 


s 


n 


s 


n 


s 


n 


m^ 


n 


— JS 


n 


^ 


n s 


ILm 


^ 


n 


«s 


n s\ 


n' 


^ 


N 












s' 


w 














s 



Fig. 49. 

put together, so that their like poles all face one way. 
Such an arrangement is indicated in Fig. 49, from which 
it will be seen that if the magnet be broken asunder across 
any part, one facQ of the fracture will present only N, 



CHAP. 11.] ELECTRICITY AND MAGNETISM. 89 

poles, the other only S. poles. This would be true no 
matter how small the individual particles. 

If the intrinsic magnetisation of the steel at every 
part of a magnet were equal, the free poles would be 
found only at the ends ; but the fact that the free mag- 
netism is not at the ends merely, but diminishes from 
the ends towards the middle, shows that the intensity of 
the intrinsic magnetisation must be less towards and at 
the ends than it is at the middle of the bar. 

107. Lamellar Distribution of Magnetisrcu 
Magnetic Shells. — Up to this point the ordinary 
distribution of magnetism along a bar has been the only 
distribution considered. But it is possible to have 
magnetism distributed over a thin sheet so that the 
whole of one face of the sheet shall have one kind of 
magnetism, and the other face the other kind of magnet- 
ism. If an immense number of little magnets were 
placed together side by side, like the cells in a honey 
comb, all with their N. -seeking ends upwards, and S.- 
seeking ends downwards, the whole of one face of the 
slab would be one large flat N. -seeking pole, and the 
other face S.-seeking. Such a distribution ^5 this over a 
surface or sheet is termed a lamellar distribution, to 
distinguish it from the ordinary distribution along a line 
or bar, which is termed, for distinction, the solenoidal 
distribution. A lamellarly magnetised magnet is some- 
times spoken of as a magnetic shelL The properties 
of magnetic shells are extremely important on account of 
their analogy with those of closed voltaic circuits. 

108. Magnetic Figures. — Gilbert showed^ that if 
a sheet of paper or card be placed over a magnet, and 
iron-filings are dusted over the paper, they settle down 
in cunning lines, forming a viagitetic figure^ the generd 
form of which is shown in Fig. 50. The filings should 
be fine, and sifted through a bit of muslin ; to facilitate 
their settling in the lines, the sheet of paper should be 

X 'Hie magnetic figures were known to Lucretiu$. 



90 



ELEINIENTARY LESSONS UN [CHAP. II. 



lightly tapped-. The figures- thus obtained can be fixed 
permanently by several processes. The best of these 
consists in employing a sheet of glass which has been 
previously gummed and dried, instead of the sheet of 
paper ; after this has been placed above the magnet the 
filings are sifted evenly over the surface, and then the 
glass is tapped ; then a jet of steam is caused to play 
gently above the sheet, softening the surface of the gum, 
which, as it hardens, fixes the filings in their places. In- 




Fi.j^. 50. 

spection of the figure will show that the lines diverge 
nearly radially from each pole, and curve round to meet 
these from the opposite pole. Faraday, who made a 
great use of this method of investigating the distribution 
of magnetism in various '' fields," gave to the lines the 
name of lines of force. They represent, as shown 
by the action on little magnetic particles which set them- 
selves thus in obedience to the attractions and repulsions 



CHAP. II.] ELECTRICITY AND MAGNETISM. gt 

in the field, the resultant direction of the forces at every 
point ; for each particle tends to assume the direction of 
the magnetic induction due to the simultaneous action of 
both poles : hence they may be taken to represent the 
lines of mag7ictic indtictio7t,'^ Faraday pointed out 
that these *' lines of force " map out the magnetic fields 
showing by their position the direction of the magnetic 
force, and by their number its intensity. If a small N.- 
seeking pole could be obtained alone, and put down on 
any one of these lines of force, it v/ould tend to move 
along that line from N. to S. ; a single S. -seeking pole 
would tend to move along the line in an opposite direc- 
tion. Faraday also assigned to these lines of force 
certain physical properties (which are, however, only 
true of them in a secondary sense), viz., that they tend 
to shorten themselves from end to end, and that they 
repel one another as they lie side by side. The modern 
view, which holds that magnetism results from certain 
properties of the ^'asther" of space, is content to say 
that in every magnetic field there are certain stresses, 
which produce a tension along the lines of force, and a 
pressure across them. 

109. This method may be applied to ascertain the 
presence of ^' conseque/it poles " in a bar of steel, the 
figure obtained resembling that depicted in Fig. 51, 
Such a state of things is produced when a strip pf ver}' 
hard steel is purposely irregularly magnetised by touching 
it with strong magnets at certain points. A strip thus 
magnetised virtually consists of several magnets put end 
to end, but in reverse directions, N.-S., S.-N., etc. 

110. The forces producing attraction between unlike 
poles, and repulsion between like poles, are beautifully 
illustrated by the magnetic figures obtained in the fields 
between the poles in the two cases, as given in Figs. 

1 Or rather the component part of the magnetic inductioa resolved into 
the plane of the figure ; which is not quite the same thing, for above the 
poles the filings stand up nearly vertically to tbif plane 



9^ ELEArRNTARY LESSONS ON [chap. ii. 



52 and 53, In Fig. 52 the poles are of opposite kinds, 
and the lines of force curve across out of one pole into 
the other; while in Fig. 53, which represents the action 



Fi^. 51. 

of two similar poles, the lines of force curve away as if 
repelling one another, and turn aside at right angles. 
Musschenbroek first pointed out the essential difference 
between these two figures. 




Fig. 52. Fig- 53. 

111. Magnetic "Writing. — Another kind of magnetic 
figures was discovered by De Haldat. who wrote wth the 
pole of a magnet upon a thin steel plate (such as a saw- 
blade), and then sprinkled filings over it. The writing, 
which is quite invisible in itself, comes out in the lines 
of filings that stick to the magnetised parts ; this magic 
writing will continue in a steel plate many months. The 
author of these Lebsons has produced similar figures in 



CHAP. II.] ELECTRICITY AND MAGNETISM. 93 

iron filings by writing upon a. steel plate with the wires 
coming from a powerful voltaic battery. 

112. Surface Magnetisation. — In many cases the 
magnetism imparted to magnets is confined chiefly to 
the outer laj^ers of steel. If a steel magnet be put into 
acid so that the outer layers are dissolved awa)', it is 
found that it has lost its magnetism when only a thin 
film has been thus removed. Magnets which have been 
magnetised very thorough!)^, however, exhibit some 
magnetism in the interior. A hollow steel tube when 
magnetised is nearly as strong a magnet as a solid rod 
of the same size. If a bundle of steel plates are mag- 
netised while bound together, it will be found that only 
the outer ones are strongly magnetised. The inner ones 
may even exhibit a reversed magnetisation. 

113. Mechanical eflfects of Mag'netisation. — 
When a steel or iron bar is powerfully magnetised it 
grows a little longer than before;, and, since its volume 
is the same as before, it at the same time contracts in 
thickness. Joule found an iron bar to increase by 720^000 
of its length when magnetised to its maximum. This 
phenomenon is believed to be due to the magnetisation 
of the individual particles, which, when magnetised, tend 
to set themselves parallel to the length of the bar. This 
supposition is confirmed by the observation of Page, that 
at the moment when a bar is magnetised or demagnetised, 
a faint metallic clink is heard in the bar. Sir W. Grove 
showed that when a tube containing water rendered 
muddy by stirring up in it finely divided magnetic oxide 
of iron was magnetised, the liquid became clearer in the 
direction of magnetisation, the particles apparently setting 
themselves end-on, and allowing more light to pass be- 
tween them. A twisted iron wire tends to untwist itself 
when magnetised. A piece of iron, when powerfully mag- 
netised and demagnetised in rapid succession, grows hot, 
as if magnetisation were accompanied by internal friction. 

114. Action of Magnetism on lAght. — Faraday 



94 ELEMENTARY LESSONS ON [chap. ii. 

discovered that a ray of polarised light passing through certain 
substances in a powerful magnetic field has the direction of its 
"^abrations changed. This phenomenon, which is sometimes 
called *'The Magnetisation of Light," is better described as 
"The Rotation of the Plane of Polarisation of Light by Mag- 
netism." The amount of rotation differs in different media, 
and varies with the magnetising force. More recently Kerr 
has shown that a ray of polarised light is also rotated by re- 
flection at the end or side of a powerful magnet. Further 
mention is made of these discoveries in the Chapter on Electro- 
optics, Lesson XXXV. 

115. Physical Theory of Magnetism. — All these various 
phenomena point to a theory of magnetism very different from 
the old notion of fluids. It appears that every particle of a 
magnet is itself a magnet, and that the magnet only becomes a 
magnet as a whole by the particles being so turned as to point 
one way. This conclusion is supported by the observation that 
if a glass tube full of iron filings is magnetised, the filings can 
be seen to set themselves endways, and that, when thus once 
set, they act as a magnet until shaken up. It appears to be 
harder to turn the individual molecules of solid steel, but. when 
once so set, they remain end -on unless violently struck or 
heated. It follows from this theory that when ail the particles 
were turned end-on the limits of possible magnetisation would 
have been attained. Some careful experiments of Beetz on iron 
deposited by electrolysis entirely confirm this conclusion, and 
add weight to the theory. The optical phenomena led Clerk 
Maxv/ell to the further conclusion that these longitudinally-set 
molecules are rotating round their long axe^ and that in the 
" sether " of space there is al?o a vortical motion along the lines 
of magnetic induction ; this motion, if occurring in a perfect 
medium (as the '* cether " may be considered), producing tensions 
along the lines and pressures at right angles to them, would 
afford a satisfactory explanation of the magnetic attractions and 
repulsions which apparently act across empty space. Hughes 
has lately shown that the magnetism of iron and steel is intimately 
connected with the molecular rigidity of the material. His 
researches with the "induction balance" (Art. 438) and "mag- 
netic balance " (Art. 439) tend to prove that each molecule of 
a magnetic metal has an absolutely constant inherent magnetic 
polarity ; and that when a piece of iron or steel is apparently 
neutral, its molecules are internally arranged so as to ?ati?fy 
each other's polarity, forming closed magnetic circuits amoncrst 



CHAP. 11. ] ELECTRICITY AND MAGNETISM. 95 

tliemselves. On this view magnetising a piece of iron simply 
causes the molecules to rotate into new and symmetrical positions. 

Lesson XL — Laws of Magnetic Force. 

116. Laws of Magnetic Force. 

First Law. — Like magnetic poles repel one 
another J unlike inagnetic poles attract one 
another. 

Second Law. — The force exerted between two 
7nagrietic poles is propoTtional to the product 
of their strengths^ and is inversely propor- 
tional to the square of the distance between 
thetn, 

117. The Law of Inverse Squares. — The second 
of the above laws is commonly known as the law of 
inverse squares. The similar law of electrical attrac- 
tion has already been explained and illustrated (Art. 
16). This law furnishes the explanation of a fact men- 
tioned in an earlier Lesson, Art. 77, that small pieces 
of iron are drawn bodily up to a magnet pole. If a 
small piece of iron wire, a b (Fig. 54), be suspended by 
a thread, and the 

N.- pointing pole 
A of a magnet be 
brought near it, 
the iron is thereby 
inductively mag- 
netised ; it turns 

round and points Pj^ 

towards the mag- 
net pole, setting itself as nearly as possible along a line 
of force, its near end b becoming a S. -seeking pole, and 
its further end a becoming a N.-seeking pole. Now the 
pole b will^be attracted and the pole a will be repelled. 
But these two forces do not exactly equal one another, 
since the distances are unequal The repulsion will 





96 ELEMENTARY LESSONS OH [cHAK It 

(by the law of inverse squares) be proportional to 

nr:A2 > ^^^ ^^^ attraction will be proportional to rr^o' 
K-^ **/ (A p)^ 

Hence the bit of iron a b will experience a pair of forces, 
turning it into a certain direction, and also a total force 
drawing it bodily toward A. Only those bodies are 
attracted by magnets in which magnetism can thus be 
induced ; and they are attracted only because of the 
magnetism induced in them. 

We mentioned, Art. 83, that a magnet needle floating 
freely on a bit of cork on the surface of a liquid, is acted 
upon by forces that give it a certain direction, but that, 
unlike the last case, it does not tend to rush as a whole 
either to the north or to the south. It experiences a 
rotation, because the attraction and repulsion of the 
magnetic poles of the earth act in a certain direction ; 
but since the magnetic poles of the earth are at a dis- 
tance enormously great as compared with the length 
from one pole of the floating magnet to the other, we 
may say that, for all practical purposes, the poles of the 
magnet are at the same distance from the N. pole of the 
earth. The attracting force on the N.-pointing pole of 
the needle is therefore practically no greater than the 
repelling force acting on the S. -pointing pole, hence 
there is no motion of translation given to the floating 
needle as a whole. 

118. Measurement of Magnetic Porcea — The 
truth of the law of inverse squares can be demonstrated 
by measuring the attraction between two magnet poles 
at known distances. But this implies that we have 
some means of measuring accurately the amount of the 
magnetic forces of attraction or repulsion. Magnetic 
force may be measured in any one of the four following 
ways: (i) by balancing it against the torsion of an 
elastic thread ; (2) by observing the time of swing of 
a magnetic needle oscillating under the influence of the 
force ; (3) by observing the deflection it produces upon a 



CHAP. II.] ELECTRICITY AND MAGNETISM. 



97 



magnetic needle which is already attracted into a cfifferent 
direction by a force of known intensity ; (4) by balanc- 
ing it against the force of gravity as brought into play 
in attempting to deflect a magnet hung by two parallel 
strings (called the bifilar suspension), for these strings 
cannot be twisted out of their parallel position without 
raising thie centre of gravity of the magnet. The first 
three of these methods must be further explained. 

119, The Torsion Balance. — Coulomb also applied 
the Torsion Balance to the measiirement of magnetic 




Fig. 55. 

forces. The main principles of this instrument (as used 
to measure electrostatic forces of repulsion) were de- 
scribed on p. 15. Fig. 55 shows how it is arranged for 

H 



98 ELEMENTARY LESSONS OK [chap, ii 

measuring magnetic repulsions. By means of the 
torsion balance we may prove the law of inverse squares. 
We may also, assuming this law proved, employ the 
balance to measure the strengths of magnet poles by 
measuring the forces they exert at known distances. 

To prove the law of inverse squares, Coulomb made 
the following experiment : — The instrument was first 
adjusted so that a magnetic needle, hung in a copper 
stirrup to the fine silver thread, lay in the magnetic 
meridian without the wire being twisted. This was done 
by first putting in the magnet and adjusting roughly, 
then replacing it by a copper bar of equal weight, and 
once more adjusting, thus diminishing the error by 
repeated trials. The next step was to ascertain through 
what number of degrees the torsion -head at the top 
of the thread must be twisted in order to drag the 
needle i"^ out of the magnetic meridian, ^n the par- 
ticular experiment cited it was found that 35° of torsion 
corresponded to the 1° of deviation of the magnet ; then 
a magnet was introduced, that pole being downwards 
which repelled the pole of the suspended needle. It was 
found (in this particular experiment) to repel the pole ol 
the needle through 24°. From the preliminary trial we 
know that this directive force corresponds to 24"* x 35** 
of the torsion -head, and to this we must add the 
actual torsion on the wire, viz., the 24°, making a total 
of 864°, which we will call the "torsion equivalent" oi 
the repelling force when the poles are thus 24** apart. 
Finally, the torsion -head was turned round so as to 
twist the suspended magnet round, and force it nearer 
to the fixed pole, until the distance between the repelling 
poles was reduced to half what it was at first. It was 
found that the torsion -head had to be turned round 8 
complete rotations to bring the poles to 12"* apart 
These 8 rotations were an actual twist of 8* x 360% 01 
2880^ But the bottom of the torsion thread was still 
twisted 12** as compared with the top, the force pro 



CHAP. 11.] ELECTRICITY AND MAGNETISM. 09 

ducing this twisi corresponding to !2 x 35 (or 420"*) of 
torsion ; and to these the actual toision of 12° must be 
added, making a total of 2880*^ + 420** -t- 12'*= 3312 
The result then of halving the distance between the 
magnet poles was to increase the force fourfohU for 
J312 is very nearly four times 864. Had the distance 
between the poles been reduced to one-third the force 
would have been nine times as great. 

120. Method of Oscillations.' — II a magnet sus- 
pended by a fine thread, or poised upon a point, be 
pushed aside from its position of rest, it will vibrate 
backwards and forwards, performing oscillations which, 
although they gradually decrease in amplitude, are 
executed in very nearly equal times. In fact, they follow 
a law similar to that of the oscillations executed by a pen- 
dulum swinging under the influence of gravity. The law 
of pendular vibrations is, that th& square of the number 
of oscillations executed in a given time is proportional to 
the force. Hence we can measure magnetic forces by 
counting the oscillations made in a minute by a magnet. 
It must be remembered, however, that the actual number 
of oscillations made by any given magnet will depend 
on the weight, lefigth, and form of the magnet, as well 
as upon the strength of its poles, and of the "field" 
in which it may be placed. 

121. We can use this method to compare the intensity 
01 the force of the earth's magnetism^ at any place with 
that at any other place on the earth's surface, by oscil- 
lating a magnet at one place and then taking it to the 
other place and oscillating it there. If, at the first, it 
makes a oscillations in one minute, and at the second, b 
oscillations a minute, then the magnetic forces at the 

Ml is possible, also» 10 measure electrical forces by a ** method of oscil- 
lations ;*' a small charged ball at the end of a horizon tally -suspended arm 
being caused to oscillate under the attracting force of a charged conductoi 
near it, whose " force" at that distance is proportional to the square of the 
number of oscillations in a given time. 

^ Or, more strictly, of its horizontal component. 



lOO 



ELEMENTARY LESSONS ON [cil.p. ii. 



two places will be to one another in the ratio of a^ 
to b\ 

Again, we may use the method to compare the force 
exerted at any point by a magnet near it with the force 
of the earth's magnetism at that point. For, if we swing 
a small magnetic needle there, and find that it makes m 
oscillations a minute under the joint action ^ of the earth's 
magnetism, and that of the neighbouring magnet, and 
that, when the magnet is removed, it makes n oscillations 
a minute under the influence of the earth's magnetism 
alone, then irfi will be proportional to the joint forces, 
;/2 to the force due to the earth's magnetism, and the 
difference of these, or v"^ -^ it^ will be proportional to the 
force due to the neighbouring magnet. 

122. We will now apply the method of oscillations to 
measure the relative quantities of free magnetism at 
different points along a bar magnet. The magnet to 
be examined is set up vertically (Fig. 56). A small 
magnet, capable of swinging horizontally, is brought near 
it and set at a short distance away 
from its extremity, and then oscillated, 
while the rate of its oscillations is 
counted. Suppose the needle were 
such that, when exposed to the earth's 
magnetism alone, it would perform 3 
complete oscillations a minute, and 
that, when vibrating at its place near 
the end of the vertical magnet it 
oscillated 14 times a minute, then 
the force due to the magnet will be 
proportional to 1 4^ — 3^ == 1 96 — 9 = 
187. Nextly, let the oscillating mag- 
net be brought to an equal distance 
opposite a point a little away from 
the end of the vertical magnet. If, here, it oscillated 

1 We are here assuming that the magnet is so placed that its force is m a 
line with that of the earth's magnetism at the point, and that the other pole 
of the magr/et is so far away as not to affect the oscillating needle. 



Fig. 56. 



CHAP. II.] ELECTRICITY AND MAGNETISM. loi 

12 times a minute, we know that the force will be pro- 
portional to I 2-— 3-= 144 — 9 = 135. So we shall find 
that as the force falls off the oscillations will be fewer, 
until, when we put the oscillating magnet opposite the 
middle of the vertical magnet, we shall find that the 
nu'^ber of oscillations is 3 per minute, or that the 
earth's force is the only force affecting the oscillations. 
In Fig. 57 we have indicated the number of oscillations 
at successive points, as 14, 12, 10, 8, 6, 5, 4, and 3. 
If we square these numbers and subtract 9 from each, 
we shall get for the forces at the various points the 
following: — 187, 135, 91, 55, 27, 16, 7, and o. These 
forces may be taken to represent the strength of the 
free magnetism at the various points, and it is convenient 
to plot them out graphically in the manner shown in 

^ 






hn IT) -. 

QO 10 O) 



Fig. 57- 

Fig. 57, where the heights of the dotted lines are chosen 
to a scale to represent proportionally the forces. The 
curve which joins the tops of these " ordinates '' shows 
graphically how the force, which is greatest at the end, 
falls off toward the middle. On a distant magnet pole 
these forces, thus represented by this curvilinear triangle, 
would act as if concentrated at a point in the magnet 



102 



ELEMENTARY LESSONS ON Cchap. n. 



opposite the ^' centre of gravity " of this triangle ; or, in 
other words, the " pole,'^ which is the centre of the result- 
ant forces, is not at the end of the magnet. In thin 
bars of magnetised steel it is at about ^ of the magnet's 
length from the end. 

123. Method of Deflections. — There are a numbei 

of ways in which the deflection of a magnet by another 

magnet may be made use of to measure magnetic forces.^ 

We cannot here give more than a glance at first principles. 

When two equal and opposite forces act on the ends of 

a rigid bar they simply tend to turn it round. Such a 

J pair of forces form what 

is called a " couple," and 

the effective power or 

" moment " of the couple 

is obtained by multiplying 

one of the two forces by 

the perpendicular distance 

between the directions of 

the forces. Such a couple 

tends to produce a motion 

of rotation, but not a 

motion of translation. 

Now, a magnetic needle 

placed in a magnetic field 

across the lines of force, 

experiences a " couple," 

tending to rotate it round 

^^s- 58. into the magnetic meridian, 

for the N. - seeking pole is urged northwards, and 

the S.-seeking pole is urged southwards, with an equal 

and opposite force. The force acting on each pole 

is the product of the strength of the pole and the 

intensity of the " field," that is to say, of the horizontal 

component of the force of the earth's magnetism at the 

1 The student desirous of mastering these methods of measuring magnetic 
forces should cpnsult Sir G. Airy's Treatise on Magnetism* 



•Vfi— 




CHAP. 11.] FXECTRICTTY AND MAGNETISM. 103 



place.' We will call the strength of the N.- seeking pole 
m; and we will use the symbol H to represent the 
force exerted in a horizontal direction by the earth's 
magnetism. (The value of H is different at different 
regions of the globe.) The force on the pole A (see 
^i^- 5^) will be then 7n x H ox m H, and that on pole 
B will be equal and opposite. We take N S as the 
direction of the magnetic meridian, and the forces will 
be parallel to this direction. Now, the needle A B lies 
obliquely in the field, and the magnetic force acting on 
A is in the direction of the line P A, and that on B in 
the direction Q B, ^s shown by the arrows. P Q is the 
perpendicular distance ^between these forces ; hence the 
'^ moment " of the couple will be got by multiplying the 
length P. O by the force exerted on one of the poles. 
Using the symbol G for the moment of the couple we 
may write 

G= PQ X ;;rH. 
But P Q is equal to the length of the magnet multiplieql 
by the sine ^ of the an^le A O R, which is the angle of 
deflection, and which we will call 8. Hence, using / for 
the length between tlie poles of the magnet, we may 
write the expression for the moment of the couple. 
G = 7n /H* sin S. 
In words this is : the *• moment of the couple " acting 
on the needle is proportional to its " magnetic moment," 
{in X /) to the horizontal force of the earth's magnetism, 
and to the sine, of the angle of deflection. 

The reader will not have failed to notice that if the 
needle were turned more obliquely, the distance P Q 
would be longer, and would be greatest if the needle 
were turned round enst-and-west, or in the direction EW. 
Also the '^ moment " of the couple tending to rotate the 
magnet will be less and less as the needle is turned 
more nearly into the direction N S. 

1 If any reader is unacquainted with tris^onometrical terms he should con 
suit the note at the end of this Lesson, on " Ways of reckoning Angles. ' 



104 ELEMENTARY LESSONS ON [chap, ii 



124. Now, let us suppose that the deflection S were 
produced by a magnetic . force applied at right angles to 
the magnetic meridian, and tending to draw the pole A 
in the direction R A. The length of the line R T multi- 
plied by the new force will be the ^^ moment " of the 
new couple tending to twist the magnet into the direction 
EW. Now, if the needle has come to rest in equilibrium 
between these two forces, it is clear that the two oppos- 
ing twists are just equal arid opposite in power, or that 
the moment of one couple is equal to the moment of the 
other couple. Hence, the force in the direction W E 
will be to the force in the direction S N in the same 
ratio as P Q is to R T, or as P O is to R O. 

Or, calling this force /J 

/: H = PO : RO 
Or /-H|2^ 

But P O = A R and ^ = tan 8 hence 
/= H tan S; 

or, in other words, i/ie viagfietic fofce which^ adhig at 
right angles to the meridian^ p7'odtices on a magnetic 
needle the deflection 5, is equal to the horizontal force oj 
the earth^s magnetism at that pointy mtdtiplied by the 
tangent of the angle of deflection. Hence, also, two 
different magnetic forces acting at right angles to the 
meridian would severally deflect the needle through 
angles whose tangents are proportional to the forces. 

This very important theorem is applied in the con- 
struction of certain galvanometers (see Art. 199). 

The name Magnetometer is given to any magnet 
specially arranged as an instrument for the purpose 
of measuring magnetic forces by the deflections they 
produce. The methods of observing the absolute 
values of magnetic forces in dynes or other abstract 
units of force will be explained in the Note at the end of 



CHAP. II.] ELECTRICITY AND MAGNETISM. 105 

Lesson XXV. See also Sir George Airv's Treatise on 
Magnetism, 

125. Unit Streng-th of Pole.— We found in Cou- 
lomb's torsion-balance a convenient means of comparing 
the strengths of poles of different magnets ; for the force 
which a pole exerts is proportional to the strength of the 
pole. The Second Law of Magnetic Force (see Art. 
116) stated that the force exerted between two poles 
was proportional to the product of their strengths, and 
was inversely proportional to the square of the distance 
between them. It is possible to choose such a strength 
of pole that this proportionality shall become numerically 
an equality. In order that this may be so, we must 
adopt the following as our unit of strength of a pole, or 
unit magnetic pole : A Unit Magnetic Pole is one oj such 
a strength tliat^ when placed at a distance of one centi- 
metre from a similar pole of eq.ual strength it repels it 
7vith a force of one dyne (see Art. 255). If we adopt 
this definition we may express the second law of magnetic 
foice in the following equation : — 

where / is the force (in dynes), ;// and 7n the strengths 
of the two poles, and d the distance between them (in 
centimeties). This subject is resumed in Lesson XXV., 
Art. 310, on the Theory of Llagnetic Potential. 

126. Theory of Magrnetio Curves. — We saw (Art. 
108) that magnetic figures are produced by iron-filings 
setting themselves in certain directions in the field of 
force aiound a magnet. We can now apply the law of 
inverse squares to aid as in determining the direction 
in which a filing will set itself at any point in the field. 
Let N S (Fig. 59) be a long thin magnet, and P any 
point in the field due to its magnetism. If the N.- 
seeking pole of a small magnet be put at P, it will be 
attracted by S and repelled by N ; the directions of these 
two foices will be along the lines P S and P N. The 



io6 ELEMENTARY LESSONS ON [chap. ii. 

amounts of the forces may be represented by certain 
lengths marked out along these lines. ' . Suppose the 
distance P N is twice as great as P S, the repelling force 
along P N will be ^ as strong as the attracting force 
along P S. So measure a distance out, P A towards S 
four times as long as the length P B measured along P N 
away from N. Find the resultant force ^ in the usual 
way of compounding mechanical forces, by completing 
the parallelogram pare, and the diagonal P R represents 
by its length and direction the magnitude and the 




Fig. 59- 

direction of the resultant magnetic force at the point P. 
In fact the line P R represents the line along which a 
small magnet or an iron filing would set itself. In a 
similar way we might ascertain the direction of the lines 
of force at any point of the field. The little arrows in 
Fig. 59 show how the lines of force start out from the N. 
pole and curve round to meet in the S. pole. Th^ 
student should compare this figure with the lines of 
filings of Fig. 50. 

^ See Balfour Stewart's Lessons in Elei)tentary Physics^ page 26 ; or 
Todhunter's Natural Philosophy /or Beginners, page 55. 



CHAP, ii.l ELECTRICITY AND MAGNETISM. 107 

127. Force due to a Magnetic ShelL-r-A mag. 
netic shell (Art. 107) exerts a magnetic force upon a mag- 
net pole placed at a point in its neighbourhood. If the 
shell be flat and very great, as compared with the distance 
of the point considered, this force will be independent of 
that distance, will be normal to the shell in direction, and 
v/ill depend only upon the amount of magnetism on the 
shell, and will be numerically equal to 27r times the 
quantity of magnetism per square centimetre ^ {i,e, to 
2 0-0- when cr is the "surface density" of magnetism on 
the face of the shell). 

'If the shell is bounded, however, by a limiting area, 
the force exerted by a shell upon a point outside it will 
be^^greater near to the shell than at a distance away. 
In this case it is most convenient to measure not the 
force but the potential due to the shell. The defini- 
tion of " magnetic potential " is given in Art. 310 ; mean- 
time we may content ourselves with stating that the 
'potential dice to a magnetic shell at a point near it^ is 
equal to the strength of the shell multiplied by the solid 
angle^ subte7ided by the shell at that point. 

1^3. A Magnetic Paradox. — If the N.-seeking 
pole of a strong magnet be held at some distance from 
the N.-seeking pole of a weak magnet, it will repel it ; 
but if it is pushed up quite close it will be found now to 
attract it. This paradoxical experiment is explained 
by the fact that the magnetism induced in the weak 
magnet by the powerful one will be of the opposite kind, 
and will be attracted ; and, when the powerful magnet is 
near, this induced magnetism may overpower and mask 
the original magnetism of the weak magnet The 
student must be cautioned that in most of the experi- 
metits on magnet poles similar perturbing causes are at 
work. The magnetism in a magnet is not quite ^xed^ 

i The proof of this proposition is similar to that given at end of Lesson 
XX., for the analogovis proposition concerning the forte due to a flat plate 
charged with electricity, 

8 See Note on *' Ways of Reckoning Angles," at the end of this Lesson. 



io8 ELEMENTARY LESSONS ON [chap. ii. 



but is liable to be disturbed in its distribution by the 
near presence of other magnet poles, for no steel is so 
hard as not to be temporarily affected by ma^^netic 
induction. The law of inverse squares is only true when 
the distance between the poles is so great that the dis- 
placement of their magnetism due to mutual induction 
is so small that it may be neglected. 



Note on Ways of Reckoning Angles and 

Solid-angles. 

129. Reckoning in Degrees. — When two straight lines cross 
one another they form an angle between them ; and this angle 
may be defined as the amount of rotation which one of the Hnes 
has performed round a fixed point in the other line. Thui we 

may suppose the line C P in Fig. 60 to 
have originally lain along GO, and then 
turned round to its present position. The 
amount by which it has been rotated is 
clearly a certain fraction of the A\hole way 
round ; and the amount of rotation round 
C we call '*the angle which PC makes 
with O C," or more simply '^ the angle 
P C O." But there are a number of 
different ways of reckoitin^ this angle. 
The common way is to reckon the angle 
by ''degrees" of arc. Thus, suppose a circle to be drawn 
round C, if the circumference of the circle were divided into 
360 parts each part would be called **one degree" (l°), and 
the angle would be reckoned by naming the number of such 
degrees along the curved arc O P. In the figure the arc is 

about 57i°, or ^ of the whole way round, no matter what size 

the circle is drawn. 

130. Reckoning in Radians. — A more sensible but less 
usual way to express an angle is to reckon it by the ratio between 
the length of the curved arc that ''subtends" the angle and the 
length of the radius of the circle. Suppose we have drawn 
round the centre C a circle whose raditis is one centimetre, 
the diameter will be two centimetres. The length of the 
circumference all round is known to be about 3} times the 

length of the diameter, or more exactly 3'I4IS9 

This number is so awkward that, for convenience, we always 




CHAP. II.] ELECTRICITY AND MAGNETISM. 



109 



Hse for it tlie Greek letter tt. Hence the length of the circum- 
ference of our circle, whose radius is one centimetre, will be 
6'283i8 . . . centimetres, or 27r centimetres. We can then 
reckon any angle by naming the length of arc that subtends it 
on a circle one centimetre in radius. If we choose the angle 
P C O, such that the curved arc O P shall be just one centimetre 
long, thisi will be the angle 07ie^ or unit of angular measure, or, 
as it is solnetimes called, the angle PCO will be 07te ** radian''' 

All the 



° 17' nearly. 

A right-angle will be 



In degree-measure one radian = = 57 

way round the circle will be 27r radians. 

~ radians-. 

-131. Rebkoning by Sines or Cosines. — In trigonometry 
other ways of reckoning angles are used, in which, however, the 
angles themselves are not reckoned, but 
certain ^^functions" of them called **sines," 
*' cosines," ^'tangetits," etc. For readers 
not Accustomed to these we will briefly ex- 
plain the geometrical nature of these 
^^ftmetions."'' Suppose we draw (Fig. 61) 
our circle as before round centre C, and 
then dpp down a plurfib-line P M, on 
to the line CO; we will, instead of reckon- 
ing the angle by the curved arc, reckon it 
by the length of the line P M. It is clear' 
that if the angle is small P M will be short ; 
opens out towards_ji right angle, P M' will 
fonger (Fig. 62). ~ 




Fig. 61. 



but as the angle 
get longer and 
The ratio between the length of this line and 
the radius of the circle is called the *' j/;?<?" 
of the angle, and if the radius is I the 
length of P M will be the value of the sine. 
It can never be greater than i, though it 
may have all values between i and - i. 
The * length of the line C M will also 
depend upon the amount of the angle. If 
the angle is small C M will be nearly as 
Ions as CO; if the angle open out to -nearly a right angle 
C M will be very short. The length of C M (when the radius 
is I) is called the '' cosirte'' of the aiigle. If the angle be 
called e, then we may for shortness write these functions: 

Sin = ^P 

Cos. = .?l 

132. Reckoning by 'Tangents.— Suppose we draw out circle 




no 



ELEMENTARY LESSONS ON [chap, ti. 



P> 



as before (Fig. 63), but at the point O draw a straight line 
touching the circle, the tangent line at O ; 
let us also prolong C P until it meets the 
tangent line at T. We may measure the 
angle between O C and O P in terms of 
the length of the tangent O T as compared 
with the length of the radius. Since our 
radius is l, this ratio is numerically the 
length of O T, and we may therefore call 
the length of O T the ** tangent " of the 
angle O C P. It is clear that smaller angles 
will have smaller tangents, but that larger 
angles may have very large tangents ; in 
fact, the length of the tangent when PC was 
moved round to a right angle would be 
infinitely great. It can be shown that the 
ratio between the lengths of the sine and 
of the cosine of the angle is the same as the ratio between the 
length of the tangent and that of the radius ; or the tangent of 
an angle is equal to its sine divided by its cosine. The formula 




Fig. 63. 



for the tangent may be written ; 

tan ^ - ^ = jjj^. 

133. Solid Angles. — \Vhen three or more surfaces intersect 
at a point they form a solid angle: there is a solid angle, for 
example, at the top of a pyramid, or of a cone, and one at every 
corner of a diamond that has 
been cut. If a surface of any 
given shape be near a point, it 
is said to subtend a certain solid 
angle at that point, the solid 
angle being mapped out by 
drawing lines from all points 
of the edge of this surface to the 
point P (Fig. 64. ) An irregular 
cone will thus be generated 
whose solid angle is the solid 
angle subtended at P by the 
surface E F, To reckon this 




Fig. 64. 



solid angle we adopt an expedient similar to that adopted when 
we wished to reckon a plane angle in radians. About the point 
P, with radius of l centimetre, describe a sphere^ which will 
intercept the cone over an area j\I N : the area thus intercepted 
measures the solid anisic If the sphere have the. radius i, its 
total surface is 47r. The solid angle subtended at the centre by 
a hemisphere would be 2ir, 



CHAP. 11.] ELECTRICITY AND MAGNETISM. 



Ill 



Table of Natural Sines and Tangents, 



Arc. 


Sine. 


Tangent. 

* 




O" 


o-ooo 


0.000 


90' 


1 


•017 


•017 


89 


2 


•035 


•035 


88 


3 


•052 


•052 


87 


4 


•070 


'O70 


86 


5 


•087 


•087 


85 


6 


•105 


•105 


84 


7 


•122 


•123 


83 


8 


•139 


•141 


82 


9 


•156 


'158 


81 


lO 


•174 


•176 


80 


'5 


•259 


•268 


75 


20 


•342 


•364 


70 


25 


•423 


•466 


65 


30 


•500 


•577 


60 


35 


•574 


•700 


55 


40 


•643 


•839 


50 


45 


•707 


I -000 


45 


50 


•766 


n92 


40 


55 


•819 


1-428 


35 


60 


•866 


1732 


30 


65 


•906 


2-145 


25 


70 


•940 


2-747 


20 


75 


•966 


3732 


15 


80 


•985 


5-671 


10 


81 


•988 


6-314 


9 


82 


•990 


7-"5 


8 


«3 


•993 


8-144 


7 


84 


•995 


9-514 


6 


85 


•996 


"•43 


5 


86 


•998 


14-30 


4 


87 


•999 


19-08 


3 


88 


•999 


28-64 


2 


89 


•999 


57-29 


I 


90 


I •000 


Infin. 







Cosine. 


Co- tangent. 


Arc. 



112 



ELEMENTARY LESSONS ON [chap. ii. 



Lesson XI L — Terrestrial Magnetism. 

134. Tlie Mariner's Compass. — It was mentioned 
in Art. 79 that the compass sold by opticians consists of 
a magnetised steel needle balanced on a fine point above 
a card marked out N, S, E, W, etc. The Mariner's 
Compass is, however, somewhat differently arranged. 

In Fig. 65 one of the forms of a Mariner's Compass, 
used for nautical observations, is shown. • Here th^ 




Fig. 65. 

card, divided out into the 32 " points of the Compass," is 
itself attached to the needle, and swings round with it so 
that the point marked N on the card always points to 
the north. In the newest and best ships' compasses 
several magnetised needles are placed side by side, as it 
is found that the indications of such a compound needle 
are more reliable. The iron fittings of wooden vessels, 
and, in the case of iron vessels, the ships themselves, 



CHAP. II.] ELECTRICITY AND MAGNETISM. ' 113 

affect the compass, which has therefore to be corrected 
by placing compensating masses of iron near it, or by 
fixing it high upon a mast. 

135. The Earth a Magnet. — Gilbert made the great 
discovery that the compass needle points north and 
south because the earth is itself also a great magnet. 
The^* magnetic poles of the earth are, however, no^ 
exactly at the geographical north and south poles. The 
magnetic north pole of the earth is more than 1000 
miles away from the actual pole, bemg in lat. 70° 5' 
N., and long. qG"* 46' W. In 1831, it was found by 
Sir J. C. Ross to be situated in Boothia Felix, just 
within the Arctic Circle. The south magnetic pole of 
the earth has never been reached ; and by reason of 
irregularities in the distribution of the magnetism there 
appear to be two south magnetic polar regions. 

136. Declination. — In consequence of this natural 
distribution the compass-needle does not at all points 
of the earth's surface point truly north and south. 
Thus, in 1881, the compass-needle at London 1 stood at 
an angle of about i8°33' west of the true north. This 
angle between the "magnetic meridian''^ and the geo- 
graphical meridian of a place is called the magnetic 
Declination of that place The existence of this 
dechnation was discovered by Columbus in 1492, though 
it appears to have been previously kno^wn to the Chinese, 
and is said to have been noticed in Europe in the early 
part of the 13th century by Peter Pellegrinus. The 
discovery is also claimed, though on doubtful authority, 
for Sebastian Cabot of Bristol. The fact that the 
declination differs at different points of the earth's sur- 
face, is the undisputed discovery of Columbus, 

in order that ships may steer by the compass, mag- 

* The Magnetic Meridian of any place, is an imaginary plane drav/B 
through che zenith, and passing through the magnetic north point and mag- 
netic south poini of the horizon, as observed at that place by the pointing o^ 
a horizontally-suspended compass-needle. 

A 



114 



ELEMENTARY LEwSSONS ON [chap, ii. 



netic charts (Art. 139) must be prepared, and the declina- 
tion at different places accurately measured. The upright 
pieces P P', on the " azimuth compass " drawn in Fig. 
65, are for the purpose of sighting a star whose position 
may be known from astronomical tables, and thus 
affording a comparison between the magnetic meridian 
of the place and the geographical meridian, and of 
measuring the angle between them. 

137. Inclination or Dip. — Norman, an instrument- 
maker, discovered in. 15 76 that a balanced needle, 
when magnetised, tends to dip downwards toward the 

north. He there- 
fore constructed a 
Dipping -Needle, 
capable of turning 
in a vertical plane 
about a horizontal 
axis, with which he 
found the << dip " 
to be (at London) 
an angle of 71° 50'. 
A simple form of 
Dipping-needle is 
shown in Fig. 66. 
The dip - circles 
used in the mag- 
netic observatory 
at Kew are much 
more exact and 
delicate instru- 
ments. It was, 




Fig. 66. 



however, found thatj:he dip, Uke the declination, differs 
at different parts of the earth's surface, and that it 
also undergoes changes from year to year. The " dip " 
in London for the year i88iwas67'' 39'. At the 
north magnetic pole the needle dips straight down. 
•The following table gives particulars of 'the Declination^ 



CHAP. II.] ELECTRICITY AND MAGNETISM. 



"5 



Inclination, and total magnetic force at a number of 
important places, the values being approximately true 
for the year 1880. 

Table of Magnetic Declination and Inclination 
(for Year 1880.) 





Declination. 


Inclination. 


Total force (in 
C. G. S.units,). 


Boothia Felix 


(None.) 


90° N 


•65 


London 




18° 40' W 


67° 40' N 


•47 


St. Petersburg 




0° 40' W 


70° N 


•48 


Berlin . 




ii°3o' W 


64° N 


•48 


Paris . 






16° 45' W 


66° N 


•47 


Rome . 






11° 30' W 


60' N 


•45 


New York 






f sf w 


72'' 12'N 


•61 


Mexico 






r ss' E 


45' ? N 


•48 


Quito . 






f 40' E 


25° ? N 


•35 


St. Helena 






26' 2$' W 

30° 2' \v 


28° S 


•31 


Cape Town 






56" 30' s 


•36 


Sydney 






9: 30' E 


62° 45' S 


•57 


Hobarton 






8° 49' E 


71° 5' S 


•04 


Tokio . 






4°S' W 


50° N 


•45 



138. Intensity. — Three things must be known in 
order to specify exactly the magnetism at any place ; 
these three elements are : 

The Declination ; 

The Inclination, and 

The Intensity of the Magnetic Force. 

The magnetic force is measured by one of the 
methods mentioned in the preceding Lesson. Its 
direction is in the line of the dipping-needle, which, like 
every magnet, tends to set itself along the lines-of-force. 
it is, however, more convenient to measure the force 
not in its total intensity in the line of the dip, but to 
measure the horizontal component of the force, — that 
is to say, the force in the direction of the horizontal 
compass -needle, from which the total force can be 



Ii6 ELEMENTARY LESSONS ON [chap. ii. 

calculated it the dip is known. Or if the horizontal 
and vertical components of the force are known, the 
total force and the angle of the dip can both be cal- 
culated The horizontal component of the force, or 
" horizontal intensity," can be ascertained either by the 
method of Vibrations or by the method of Deflexions. 
The mean horizontal force of the earth's magnetism at 
London in 1880 was 'iS dyne-units, the total force (in 
the line of dip) is '47 dyne-units. The distribution of 
the magnetic force at different points of the earth^s 
surface is irregular, and varies in different latitudes 
according to an approximate law, which, as given by 
I3iot, is that the force is proportional to Vi + 3 sin^A 
where / is the magnetic latitude. 

139. Magnetic Mapa — For purposes of conveni- 
ence it is usual to construct magnetic maps, on which 
such data as these given in the Table on p. 115 can be 
marked dowa Such maps may be constructed in 
several ways. A useful way of marking the map is to 
find out those places at which the declination is the 
same, and to join these places by a line. Such lines are 
called isogenic lines. The magnetic map of the United 
States, in the front of this volume, is constructed on this 
plan. In certain parts of the earth the magnet coincides 
with the geographical meridian. These points are cor- 
rected by an irregularly curved imaginary line, called a 
line of no variation or agonic line. The line cuts the east 
of South America, and, passing east of the West Indies, 
enters North America near Charleston, and traverses 
Hudson's Bay; thence it passes through the North 
Pole, entering the Old World east of the White Sea, 
traverses the Caspian, cuts the east of Arabia, turns then 
toward Australia and passes through the South Pole, to 
join itself again. This line is slowly moving westward. 

Maps on which such isogenic lines are depicted are 
called declination or variation maps. Since the ele- 
ments of the earth's magnetism are continually 
changing, the lines can only be determined for 



CHAP. II.] ELECTRICITY AND MAGNETISM. 



117 



a definite time. We might similarly construct a 
magnetic map, marking it with lines joining places 
where the dip was equal ; such hnes would be called 
Isoolinic lines. In England they run across the map 
from west-south-west to east-north-east. On the globe 




Fig. 67. 

the isogonic lines run for the most part from the north 
magnetic pole to the .south magnetic polar region, but, 
owing to the irregularities of distribution of the earth's 
magnetism, their forms are not simple. The isoclinic 
lines of the globe run round the earth like the parallels 



Ii8 ELEMENTARY LESSONS ON [chap. n. 

of latitude, but are irregular in form. Thus the line 
joining places where the north-seeking pole of the 
needle dips down 70** runs across England and Wales, 
passes the south of Ireland, then crosses the Atlantic in 
a south-westerly direction, traverses the United States, 
swerving northwards, and just crosses the southern tip 
of Alaska. It drops somewhat southward again as it 
crosses China, but again curves northwards as it enters 
Russian territory. Finally it crosses the southern part 
of the Baltic, and reaches England across the German 
Ocean. The chart of the world, given in Fig. 67, shows 
the isoclinic lines of the Northern Hemisphere, and also 
a system of ** terrestrial magnetic meridians " meeting 
one another in the North Magnetic pole at A. ItVas 
prepared by the Astronomer-Royal, Sir George Airy, for 
his Treatise on Magnetism, 

140. Variations of Earth's Magnetism. — We 
have already mentioned that both the declination and 
the inclination are subject to changes ; some of these 
changes take place very slowly, others occur every year, 
and others again eVery day. 

141. Secular Changes.— Those changes which re-' 
quire many years to run their course are called secular 
changes. 

The variations of the decli7iaiion previous to 1580 
are not recorded ; the compass at London then pointed 1 1** 
east of true north. This easterly declination gradually de- 
creased, until in 1657 the compass pointed true north. 
It then moved westward, attaining a maximum of 24*" 
27' about the year 18 16, from which time it has slowly 
diminished, but at a decreasing rate; it diminishes now 
(in England) at about the rate of 7' per year. At 
about the year 1976 it will again point truly north, 
making a complete cycle of changes in about 320 years. 

The Jjiclitiation in 1576 was 71° 50', and it slowly 
increased till 1720, when the angle of dip reached 
the maximum value of 74** 42'. It has since steadily 



CHAP. II.] ELECTRICITY. AND MAGNETISM. 



119 



diminished to the value of 67'' 13' in 1897. The period in 
which the cycle is eompletect is not known, but the rate 
of variation of the dip is less at the present time than it 
was fifty years ago. In all parts of the earth both declin- 
ation and inclination are changing similarly. The follow- 
ing table gives the data of the secular changes at London. 

Table of Secular Magnetic Variations. 



Ye^ar. 


Declination. 


Inclination. 


1576 




71° so' 


1580 


II" i/E. 




1600 




72' 0' 


1622 


6" 12' 




1^34 


4^0 




1657 


0° 0' min. 




1676 


3"o'W. 


73° 30' 


1705 


9°o' 




1720 


^fo 


74" 42' max. 


1760 


IQ^30' 




1780 




72° 8' 


■1800 


24° 6' 


70° 35' 


1816 


2r 30' max. 




1830 


24' 2 


69° 3' 


185s 


23° 0' 




1868 


20° 35' 


68-2' 


1878 


19° 14 


67' 43' 


1880 


j8' 40' 


67» 40 


1897 


17° 5'. 


67°i3' 



The Tofa/ Maij^nctic force^ or ** Intensity," also 
slowly changes in value. As measured near London it 
was equal to '4791 dyne-units in 1848, -4740 in 1866, 
and at the beginning of 1880, '4736 dyne-units.^ Owing 
to the steady decrease of the angle at which the needle 
dips, the horizontal component of this force (/>. the 
" Horizontal Intensity ") is slightly increasing. It was 
•17 16 dyne-units in 1848, and -1797 dyne-units at the 
be'ginning of 1880. 

^ That is to say, a north magnet pole of unit stren.::th is urged in ilie hue 
of Jip, with a mechanical force of a litlh- less than half a Jyi\<» 



I20 ELEMENTARY LESSONS ON [ruAP. u 



142. Daily Variations. — Both compass and dipping 
needle, if minutely observed, exhibit slight daily motions. 
About 7 a.m. the compass needle begins to travel west 
v/ard with a motion which lasts till about i p.m. ; during 
Lhe afternoon and evening the needle slowly travels back 
eastward, until about lo p.m. : after thi^ it rests quiet ; 
but in summer-time the needle begins to move again 
slightly to the west at about midnight, nnd returns again 
eastward before 7 a.rii. These delicate variations— never 
more than 10' of arc — appear to be connected with the 
position of the sun ; and the moon also exercises a 
minute influence upon the position of the needle. 

143. Annual Variations. — There is also an annual 
variation corresponding with the movement of the earth 
around the sun. In the British Islands the total force 
is greatest in June and least in February, but in the 
Southern Hemisphere, in Tasmania, the reverse is the 
case. The dip also differs with the season of the year, 
the angle of dip being (in England) less during the four 
summer months than in the rest of the year. 

144. Eleven -Year Period. — General Sabine djs 
covered that there is a larger amount of variation of the 
declination occurring about once every eleven years. 
Schwabe noticed thaf the recurrence of these periods 
coincided with the eleven -year periods at which there 
is a maximum oi spots on the sun. Professor Balfour 
Stewart and others have endeavoured to trace a similar 
periodicity in the recurrence of auroras^ and of other 
phenomena. 

145. Magnetic Storms. — It is sometimes observed 
tliat a sudden (though very minute) irregular disturbance 
will affect the whole of the compass needles over a con- 
siderable region of the globe. Such occurrences are 
known as magnetic storms ; they frequently occur at 
Ihe time when an aurora is visible. 

146. Self-recording' Mag'notic Apparatus. — At 

I See Lesson XXIV., on Atmospheric Electricity. 



CHAP. ii.J ELECTRICITY AND MAGNETISM. 121 

Kew and other magnetic observatories the daily and 
hourly variations of the magnet are recorded on a 
continuous register. The means employed consists in 
throwing a beam of light from a lamp on to a light mirror 
attached to the magnet whose motion is to be observed. 
A spot of light is thus reflected upon a ribbon of photo- 
graphic paper prepared so as to be sensitive to light. 
The paper is moved continuously forward by a clock- 
work train ; and if the magnet be at rest the dark trace 
on the paper will be simply a straight line. If, however, 
the magnet moves aside, the spot of light reflected from 
the mirror will be displaced, and the photographed Hne 
will be curved or crooked. Comparison of such records, 
or ** magnet ographs,^^ frotn stations widely apart on the 
earth's surface, promises to afford much light upon the 
cause of the eanh's magnetism and of its changes, of 
which hitherto no reliable origin has been with certainty 
assigned. 

The phenomenon of earth • currents (.\rt. 403) appears to he connected 
with that of the chaiig^es in the earth's magnetism, and can be observed 
whenever there is a display of aurora, and during a magnetic storm ; but it 
is not yet determined whether these currents are due to the variations in the 
magnciism of the earth, or whether these variations are due to the currents. 
It is known that the evaporation (see Art. 63) always going on in the tropics 
causes the ascending currents of heated air to be electrified positively 
relatively to the earth. These air-currrents travel northward and southward 
toward the colder polar regions, where they descend. These streams of 
electrified air will act (see Art. 337) like true electric currents, and as the 
earth rotates within them it will be acted upon magnetically. Whether this 
^\\\ account for the gradual growth of the earth's magnetism is an open 
question. The action of the sun and moon in raising tides in the atmosphere 
might also account for the variations mentioned in Art. 142. It is im- 
portant to note that in all magnetic storms the intensity of the perturbations 
is greatest in the regions nearest the poles ; also, that the magnetic poles 
coincide very nearly with the regions cf greatest cold ; that the region where 
aurorse (Art. 309) are seen in greatest abundance is a region lying nearly 
symmetrically round the magnetic pile. It may be added that the general 
direction of the feeble daily earth - currents (Art. 403) is from the pole*" 
tov/ard the equator 



122 ELEMENTARY LESSONS ON Icuap. in 



CHAPTER III. 

Current Electricity. 

Lesson XI 11. — Simple Voltaic Cells. 

147. It has been already mentioned, in Lesson IV, 
how electricity flows away from a charged body through 
any conducting substance, such as a wire or a wetted 
string. If, by any arrangement, electricity could be 
supplied to the body just as fast as it flowed away, a 
continuous cuirent would be produced. Such a current 
always flows through a conducting wire, if the ends are 
kept at different electric potentials. In like manner, 
a current of heat flows through a rod of metal if the 
ends are kept at different temperatures, the flow being 
always from the high temperature to the lower. It is 
convenient to regard electricity as flowing from positive 
to negative ; or, in other words, the direction of an electric 
current is from the high potential to the low. It is 
obvious that such a flow tends to bring both to one 
level of potential. The " current '* has sometimes been 
regarded as a double transfer of positive electricity in 
one direction, and of negative electricity in the opposite 
direction. The only evidence to support this very un- 
necessary supposition is the fact that, in the decom- 
position of liquids by the current, some of the elements 
are liberated at the point where the potential is highest, 
others at the point where it is iowest. 



CHAP. III.] ELECTRICITY AND MAGNETISM. 123 

Continuous currents of electricity, such as we have 
described, are usually produced by voltaic cellsy or 
batteries of such cells, though there are other sources of 
currents hereafter to be mentioned. 

148. Discoveries of Galvani and of Volta. — 
The discovery of electric currents originated with Galvanic 
a physician of Bologna, who, about the year 1786, made 
a series of curious and important observations upon the 
convulsive motions produced by the " return-shock " (Art. 
26) and other electric discharges upon a frog's leg. He 
was led by this to the discovery that it was not necessary 
to use an electric machine to produce these effects, but 
that a similar convulsive kick was produced in the frog's 
leg when two dissimilar metals, iron and copper, for 
example, were placed in contact with a nerve and a 
muscle respectively, and then brought into contact with 
each other. Galvani Imagined this action to be due to 
electricity generated by the frog's leg; itself. It was, 
however, proved by Volia^ Professor in the University 
of Pavia, that the electricity arose not from the muscle 
or nerve, but from the contact of the dissimilar metals. 
\Vlien two metals both in contact with the air or other 
oxidising medium are placed in contact with one another, 
the surface of one becomes positive and of the other nega- 
tive, as stated on p. 67. Thou^ the charges are very 
feeble, Volta proved their reality by two different methods. 

149. Contact Electricity: Proof by the Con- 
densing Electroscope. — The first method of proof 
devised by Volta involved the use of the Condensing 
Electroscope^ alluded to in Art. 71. It can be used in 
the following way to show the production of electrifi- 
cation. A small bar made of two dissimilar metals, zinc 
and copper soldered together, is held in the hand, and 
one end is touched against the lower plate, the upper 
plate being at the same time joined to " earth " or 
touched with the hand (Fig. 68). During the con- 
tact electrical separation has taken piace at the point 



124 



ELEMENTARY LESSONS ON [chap. hi. 



where the dissimilar metals touched one another, and 

upon the plates of 
the condenser the op° 
posite charges have 
accumulated. When 
the upper plate is 
lifted off the lower 
one, the capacity of 
the condenser dimin- 
ishes ehormously, and 
the small quantity of 
electricity is now able 
to raise the potential 
of the plates to a 
higher degree, and 
the gold leaves ac- 
cordingly expand.^ 

150. The Voltaic 
Pile. — The second of 
^^ * Volta's proofs was less 

direct, but even more convincing ; and consisted in 
showing that when a number of such contacts of dis- 
similar metals could be arranged so as to add their 
electrical effects together, those effects were more power- 
ful in proportion to the number of the contacts. With 
this view he constructed the apparatus known (in honour 
of the discoverer) as the Voltaic Pile (Fig. 69). It 
is made by placing a pair of discs of zinc and copper 
in contact with one another, then laying on the copper 
disc a piece of flannel or blotting-paper moistened with 
brine, then another pair of discs of zinc and copper, and 
so on, each pair of discs in the pile being separated 

i Formerly, this action was accounted for by saying that the electricity 
which was " bound " when the plates of the condenser were close together, 
becomes " free ** when the top plate is lifted up ; the above is. however, a 
more «icientific and more accurate way of saying the same thing. The 
student who is unable to reconcile these two v/ays of stating the matter 
snould read again Articles 47, 48, on pp. 53 to 55. 




CHAP. III.] ELECTRICITY AND MAGNETISM. 



by a moist conductor. Such a ^ile^ if composed of 
a number of such pairs of discs, will produce electricity 
enough to give quite a perceptible shock, if the top and 
bottom discs, or wires connected with 
aiem, be touched simultaneously with 
uhe moist fingers. When a single pair 
of metals are placed in contact, one 
becomes + ly electrical to a certain small 
extent, and the bther — ly electrical, or in 
other words there is a certain difference 
of electric potential (see p. 40) between 
them. But when a number are thus set 
in series with moist conductors between 
the successive pairs, the difference of 
potential between the first zinc and the 
last copper disc is increased in propor- 
tion to the number of pairs ; for now 
all the successive small differences of potential are added 
together. 

151. The Cro'wii of Oups. — Another combination 
devised by Volta was his Couronne de Tasses or Crown 
of Cups. It consisted of a number of cups (Fig. 70), 




Fig. 69. 




Fig. 70. 

filled either with brine or dilute acid, into which dipped 
a number of compound strips, half zinc half copper, 
the zinc portion of one strip dipping into one cup, while 



126 



ELEMENTARY LESSONS ON [chap. hi. 



the copper portion dipped into the other cup. The 
difference of potential between the first and last cups 
is again proportional to the number of pairs of metal 
strips. This arrangement, though badly adapted for 
such a purpose, is powerful enough to ring an electric 
bell, the wires of which are joined to the first zinc and 
the last copper strip. The electrical action of these 
combinations is, however, best understood by studying 
the phenomena of one single cup or cell. 

152. Simple Voltaic Cell. —Place in a glass jar some 
water having a little sulphuric acid or any other oxidising 
acid added to it (Fig. 71). Place in it separately two 

clean strips, one of 
zinc Z, and one of 
copper C. This cell 
is capable of sup- 
plying a continuous 
flow of electricity 
through a wire 
whose ends are 
brought into con- 
nection with the 
two strips. When 
the current flows 
the zinc strip is 
observed to waste 
away; its consump- 
tion in fact furnishes 
the energy required 
to drive the current 
through the cell 
The cell may therefore be 




Fig, 71. 



and the connecting wire, 
regarded as a sort of chemical furnace in which the fuel 
is zinc. Before the strips are connected by a wire no 
appreciable difference of potential between the copper 
and the zinc will be observed by an electrometer; 
because the electrometer only measures the potential at 



CHAP. III.) ELECTRICITY AND MAGNETISM. 12? 

a point in the air or oxidising modium outside the zinc 
or the copper, not the potentials of the metals them- 
selves. The zinc itself is at about 1-86 volts lower 
potential than the surrounding oxidising media (see Art. 
422 bis) \ while the copper is at only about -81 volts 
lower, having a less tendency to become oxidised. 
There is then a latent difference of potential of about 
1*05 volts between the copper and the zinc: but this 
produces no current as long as there is no metallic con- 
tact. If the strips are made to touch, or are joined by 
a pair of metal wnres, immediately there is a rush of 
electricity through the metal from the copper to the zinc, 
and a small portion of the zinc is at the same time dis- 
solved away ; the zinc parting with its latent energy as 
its atoms combine with the acid. This energy is ex- 
pended in forcing a discharge of. electricity through the 
acid to the copper strip, and thence through the wire 
circuit back to the zinc strip. The copper strip, whence 
the current starts on its journey through the external 
circuit, is called the positive pole^ and the zinc strip is 
called the negative pole. If two copper wires are united 
to the tops of the two strips, though no current flows so 
long as the wires are kept separate, the wire attached to 
the zinc will be found to be negative, and that attached 
to the copper positive, there being Still a tendency for 
the ainc to oxidise and drive electricity through the cell 
from zinc to copper. This state of things is represented 
in Fig^ 71 ; and this distribution of potentials led some 
to consider the junction of the zinc with the copper wire 
as the starting point of the current. But the real startiitg 
point is in the cell at the surface of the zinc where 
the chemical action is furnishing energy ; for from this 
point there are propagated through the liquid certain 
electro-chemical actions (more fully explained in chap, 
xi.) which have the result of constantly renewing the 
difference of potential and supplying electricity to the 
4- pole just as fast as that electricity leaks away through 



128 ELEMENTARY LESSONS ON Ichap. iil 

the wire to the — pole. At the same time it will be 
noticed that a few bubbles of hydrogen gas appear on the 
surface of the copper plate. Both these actions go on as 
long as the wires are joined to form a complete circuit. 

153. Effects produced by Current. — The cur- 
rent itself cannot be see7t to flow through the wire 
circuit ; hence to prove that any particular cell or 
combination produces a current requires a knowledge 
of some of the effects which currents can produce. These 
are of various kinds. A current flowing through a thin 
wire will heat it ; flowing near a magnetic needle it will 
cause it to turn; flowing through water and other 
liquids it decomposes them ; and, lastly, flowing through 
the living body or any sensitive portion of it, it produces 
certain sensations. These effects, thermal, magnetic, 
chemical, and physiological, will be considered in special 
Lessons. 

154. Voltaic Battery. — If a number of such simple 
cells are united in series, the zinc plate of one joined to 
the copper plate of the next, and so on, a greater differ- 
ence of potentials will be produced betv/een the copper 
*' pole " at one end of the series and the zinc *' pole " at 
the other end. Hence, when the two poles are joined 
by a wire there will be a more powerful flow of electricity 
than one cell would cause. Such a combination of 
Voltaic Cells is called a Voltaic Battery.^ 

155. Electromotive -Force, — The term ^^ eleciro- 
motive-force " is employed to denote that which moves 
or tends to move electricity from one place to another.^ 

1 By some writers the name Galvaitic Battery i«; given in honour of 
Galvani ; but the honour is certainly Volta's. The electricity that flows 
thus in currents is sometimes called l^oitaic Electricity, or Galvanic 
Electricity^ or sometimes even Galvanism (!), but, as we shall see, it differs 
only in degree from Frictional or any other Electricity, and both can flow 
through wires, and magnetise iron, and decorapope chemical compoundx. 

2 The beginner must not confuse " Electromotive •forcey'* or that which 
tends to move electricity, with Electric *^ force,'" or that force with 
which electricity tends to move inc.tter. Newton has virtually defined 
** force," once for all, as that which moves or tend& to move matter When 



CHAP. iii.J ELECTRICITY AND MAGNETISM. 129 

For brevity w^ sometimes write it E.M.F. In this 
particular case it is obviously the result of the difference 
of potential, and proportional to it. Just as in water- 
pipes a difference oj level produces a pressure^ and the 
pressure produces d^flow so soon as the tap is ttamed 
on, so difference of polential produces eleclromotive-force^ 
and electromotive-force sets up a current so soon as a 
circuit is completed for the electricity to flow through. 
Electromotive-force, therefore, may often be conveniently 
"expressed as a difference of potential, and vice versd, 
but the student must not forget the distinction. 

156. Volta's Laws.— Volta showed (Art 7 1 ) that 
the difference of potential between two metals in contact 
depended merely on what metals they were, not on 
their size, nor on the amount of surface in contact. He 
also showed that when a number of metals touch one 
another the difference of potential between the first and 
last of the row is the same as if they touched one 
another directly. A quantitative illustration from the 
researches of Ayrton and Perry was given in Art. 72. 
But the case of a series of cells is different from that of 
a mere row of metals, for, as we have seen, when two 
metals are immersed m a conducting liquid they are 
thereby equalised, or nearly equalised, in potential 
Hence, if in the row of cells the zincs and coppers are 
all arranged in one order, so that all of them set up 
electromotive -forces in the same direction, the total 
electromotive 'force of the series will be equal to the 
electromoii^je 'force of one cell mtdtiplied by fhe number 
jf cells. 

157. Hitherto we have spoken only of zinc and 
copper as the materials for a battery ; but batteries may 
be made of any two metals. That battery will have the 

matter is moved by a magnet we speak rightly of magnetic forct ; wheo 
electricity moves matter we may speak of electric force. But E.M.F. is 
quite a different thing, not **^force" at all. for it acts not on matter but on 
electricity, and tends tn move it. 

K 



$30 ELEMENTARY LESSONS ON [chap. hi. 

greatest electromotive -force, or be the most "intense," 
in which those materials are used which give the 
greatest difference of potentials on contact, or which are 
widest apart on the ** contact-series " given in Art. 72. 
Zinc and copper are very convenient in this respect ; 
and zinc and silver would be better but for the expense. 
For more powerful batteries a zinc-platinum or a zinc- 
carbon combination is preferable. 

168. Resistance. — The same electromotive -force 
does not, however, always produce a current of the same 
strength. The strength of the current depends not only on 
the force tending to drive the electricity round the circuit, 
but also on the resistance which it has to encounter 
and overcome in its flow. If the cells be partly choked 
with sand or sawdust (as is sometimes done in so- 
called ** Sawdust Batteries " to prevent spilling), or, if the 
wire provided to complete the circuit be very long or 
very thin, the action will be partly stopped, and the 
current will be weaker, although the E.M.F. may be 
unchanged. The analogy of the water-pipes will again 
delp us. The pressure which forces the water through 
pipes depends upon the difference of level between the 
cistern from which the water flows and the tap to which 
it flows ; but the amount of water that runs through will 
depend not on the pressure alone, but on the resistance 
it meets with ; for, if the pipe be a very thin one, 01 
choked v/ith sand or sawdust, the water will only run 
slowly through. 

Now the metals in general conduct well : their resist- 
ance is small ; but metal wires must not be too thin or 
too long, or they will resist too much, and permit only 
a feeble current to pass through them. The liquids in 
the battery do not conduct nearly so well as the metals, 
and different liquids have different resistances. Pure 
water will hardly conduct at all, and is for the feeble 
electricity of the voltaic battery almost a perfect in- 
sulator, though for the high- potential electricity of the 



CHAP. rn.J ELECTRICITY AND MAGNETISM ^31 

fiictional machines it is, as we have seen, a fair conductor. 
Salt and sahpetre dissolved in water are good con- 
ductors, and so are dilute acids, though strong sul- 
phuric acid is a bad conductor. The resistance of the 
liquid in the cells may be reduced, if desired, by using 
larger plates of metal and putting them nearer together. 
Gases are bad conductors ; hence the bubbles of hydro- 
gen gas which are given off at the copper plate durin^^ 
the action of the cell, and which stick to the surface 
of the copper plate, increase the internal resistance of 
the cell by diminishing the effective surface of the plates. 



Lesson XIV. — Chemical Actions in the Ceil. 

159. The production of a current of electricity in a 
voltaic cell is always accompanied by chemical actions 
in the cell. One of the metals at least must be readily 
oxidisable, and the liquid must be one capable of acting 
on the metal. As a matter of fact, it is found that zinc 
and the other metals which stand at the-electropositive 
end of the contact -series (see Art. 72) ^re oxidisable ; 
whilst the electronegative substances — copper, silver, 
gold, platinum, and graphite — are less oxidisable, and 
the last three resist the action of every single acid. 
There is no proof that their electrical behaviour is due to 
their chemical behaviour ; nor is their chemical behaviour 
due to their electrical. Probably both result from a 
common cause. (See Article 422 {bis), and also p. 71.) 

160. A piece of quite pure zinc when^ dipped alone 
into dilute sulphuric acid is not attacked by the liquid. 
But the ordinary commercial zinc is not pure, and when 
plunged into dilute sulphuric acid dissolves away, a large 
quantity of bubbles of hydrogen gas being given off from 
the surface of the metal. Sulphuric acid is a complex 
substance, in which every molecule is made up of a 
group of atoms, — 2 of Hydrogen, i of Sulphur, and 4 of 



^32 ELEMENTARY LESSONS ON [chap, hi 

Oxygen ; or, in symbols, HjSO^. The chemical reaction 
by which the zinc enters into combination with the 
radical of the acid, turning out the hydrogen, Is expressed 
in the following equation : — 

Zn + H2SO4 « ZnSO^ + Hg 

Zinc and Sulphuric Acid produce Sulphate of Zinc and Hj^drogen. 

The sulphate of zinc produced in this reaction remains 
in solution in the liquid. 

Now, when a plate of pure zinc and a plate ot some 
less-easily oxidisable metal — copper or platinum, or, best 
of all, carbon (the hard carbon from the gas retorts) — 
are put side by side into the cell containing acid, no 
appreciable chemical action takes place until the circuit 
is completed by joining the two plates with a wire, or by 
making them touch one another. Directly the circuit is 
completed a current flo^vs and the chemical actions 
begin, the zinc dissolving in the acid, and the acid giving 
up its hydrogen in streams of bubbles. But it wnll be 
noticed that these bubbles of hydrogen are evolved noi 
at the zinc plate, nor yet throughout the liquid, but ai the 
stirface of the copper plate (or the carbon plate if carbon 
is employed). This apparent transfer of the hydrogen 
gas through the liquid from the surface of the zinc plate 
to the surface of the copper plate where it appears is 
very remarkable. The ingenious theor}' framed by 
Grotthuss to account for it, is explained in Lesson 
XXXVIII. on Electro-Chemistr}^ 

These chemical actions go on as long as the current 
passes. The quantity of zinc used up in each cell is 
proportional to the amount of electricity which flows 
round the circuit while the batter^'' is at work ; or, in 
other words, is proportional to the strength of the 
current. The quantity of hydrogen gas evolved is also 
proportional to the amount of zinc consumed, and also 
to the strength of the cur»*ent. *\fter the acid has thus 
diseoUed zinc /in it, it will no longer act as a corrosive 



CHAP. III.] ELECTRICITY AND MAGNETISM. 133 



solvent; it has been "killed," as workmen say, for it 
has been turned into sulphate of zinc The battery will 
cease to act, therefore, either when the zinc has all dis- 
solved away, or when the acid has become exhausted, 
that is to say, when it is all turned into sulphate of zinc. 
Stout zinc plates will last a long time, but the acids 
require to be renewed frequently, the spent liquor being 
emptied out. 

161. Local Action. — When the circuit is not closed 
the current cannot flow, and there should be no chemical 
action so long as the battery is producing no current. 
The impure zinc of commerce, however, does not re- 
main quiescent in the acid, but is continually dissolving 
and giving off hydrogen bubbles. This local action, 
as it is termed, is explained in the following manner: — 
The impurities in the zinc consist of particles of iron, 
arsenic, and other metals. Suppose a particle of iron to 
be on the surface anywhere and in contact with the acid. 
It will behave like the copper plate of a battery towards 
the zinc particles in its neighbourhood, for a local differ- 
ence of potential will be set up at the point where there 
is metallic contact, causing a local current to run from 
the particles of zinc through the acid to the particle of 
iron, and so, there will be a constant wasting of the zinc, 
both when the battery circuit is closed and when it is open. 

162. Amalgamation of Zinc. — We see now why a 
piece of ordinary commercial zinc is attacked on being 
placed in acid. There is local action set up all over its 
surface in consequence of the metallic ifnpurities in it. 
To do away with this local action, and abolish the 
wasting of the zinc while the battery is at rest, it is usual 
to amalgamate the surface of the zinc plates with 
mercury. The surface to be amalgamated should be 
cleaned by dipping into acid, and then a few drops of 
mercury should be poured over the surface and rubbed 
into it with a bit of linen rag tied to a stick. The 
mercury unites with the zinc at the surface, forming a 



134 ELEMENTARY LESSONS ON [chap. in. 

pasty amalgam. The iron particles do not dissolve in 
the mercury, but float up to the surface, whence the 
hydrogen bubbles which may form speedily carry them 
off. As the zinc in this pasty amalgam dissolves into 
the acid the film of mercury unites with fresh portions 
of zinc, and so presents always a clean bright surface to 
the liquid* 

A newer and better process is to add about 4 per cent of 
mercury to the molten zinc before casting into plates or rods. 
If the zinc plates of a battery are well amalgamated there should 
be no evolution of hydrogen bubbles when the circuit' is open. 
Nevertheless there is still always a little wasteful local action 
during the action of the battery. Jacobi found that while one 
part of hydrogen was evolved at the positive pole, 33*6 parts oi 
zinc were dissolved at the negative pole, instead of the 32*5 
parts which are the chelnical equivalent, of the hydrogen. 

163. Polarisation. — The bubbles of hydrogen gas 

liberated at the surface of the copper plate stick to 

it in gr^eat numbers, and form a film over its surface ; 

hence the effective amount of surface of the copper plate 

is very seriously reduced in a short time. WTien a 

simple cell, or battery of such cells^ is set to produce a 

current, it is found that the strength of the current after 

a few minutes, or even seconds, fells off very greatlyj 

and may ^ven be almost stopped. This immediate 

falling off in the. strength of the current, which can be 

observed with any galvanometer and a pair of zinc and 

copper plates dipping into acid, is almost entirely due to 

th^ film of hydrogen bubbles sticking to the copper pole. 

A battery which is in this condition is said to be 

"polarised." 

194. Bflfeots of polarisation. — The. film of hydro- 
gen bubbles affects the strength of the current of the ceU 
in two ways. 

Firstly^ It weakens the current by the increased. r-^^/- 
a7ice which it offers to the flow, for bubbles of gas are 
bad conductors ; and, 

Secondly y It weakens th6 cjurrent by setting up an 



CHAP, ni.] ELECTRICirV AND MAGNETISM, 13S 

opposing electromotive-force J for hydrogen is almost as 
oxidisable a substance as zinc, especially when freshly 
deposited (or in a *^ nascent " state), and is electropositive, 
standing high in the series on p. 69. Hence the 
hydrogen itself produces a difference of potential, which 
would tend to start a current in the opposite direction to 
the true zinc-to-copper current. 

It is therefore a very important matter to abolish this 
polarisation, otherwise the currents furnished by batteries 
would not be constant. 

165. Remedies against Internal Polarisation. 
— Various remedies have been practised to reduce or 
prevent the polarisation of cells. These may be classed 
as mechanical, chemical, and electro-chemical. 

1. Mechanical Means, — If the hydrogen bubbles be 
siraply brushed away from the surface of the positive 
pole, the resistance they caused will be diminished. If 
air be blown into the acid solution through a tube, or if 
the liquid be agitated or kept in constant circulation by 
siphons, the resistance is also diminished. If the surface 
be rough or covered with points, the bubbles collect more 
freely at the points and are quickly carried up to the 
surface, and so got rid of. This remedy was applied in 
Smee*s Cell, which consisted of a zinc and a platinised 
silver plate dipping int<5 dilute sulphuric acid ; the silver 
plate, having its surface thus co\ered with a rough coat 
ing of finely divided platinum, gave up the hydrogen 
bubbles freely ; nevertheless, in a battery of Smee Cells 
the current falls off greatly after a few minutes. 

2. Chemical Means, — If a highly-oxidising substance 
be added to the acid it will destroy the hydrogen bubbles 
whilst they are still in the nascent state, and thus will 
prevent both the increased internal resistance and the 
opposing electromotive - force. Such substances are 
bichromate of potash, nitric acid, and bleaching powder 
(so-called chloride of lime). These substances, however, 
would attack the copper in a zinc^copper cell Hence 



136 



ELEMENTARY LESSONS ON [chap. hi. 



they can only be made use of in zinc-carbon or zinc- 
platinum cells. Nitric acid also attacks zinc when the 
circuit is open. Hence it cannot be employed in the 
same single cell with the zinc plate. In the Bichro- 
mate Battery, invented by Poggendorf, bichromate 

of potash is added 
to the sulphuric acid. 
This cell is most con- 
veniently made up as 
a " bottle battery " 
(Fig. 72), in which a 
plate of zinc is the — 
po(e, and a pair of 
carbon plates, one on 
each side of the zinc, 
are joined together at 
the top as a + pole. 
As this solution acts 
on the metal zinc 
when the circuit is 
open, the zinc plate 
is fixed to a rod by 
which it can be drawn 
up out of the solution 
when the cell is not being worked. Other cases of 
chemical prevention of polarisation are mentioned in 
describing other forms of battery. 

3. Electro-chemical Means, — It is possible by employ- 
ing double cells, as explained in the next Lesson, to so 
arrange matters that some solid metal, such as copper^ 
shall be liberated instead of hydrogen bubbles, at the 
point where the current leaves the liquid. This electro- 
chemical exchange entirely obviates polarisation. 

166. Simple Laws of Oliemical Action in the 
OelL — We will conclude this section by enumerating the 
two simple laws of rhemical action in the cell. 

1. The ainotmt of chemical action in the cell is propor^' 




Fig. 72. 



CHAP. III.] ELECTRICITY AND MAGNETISM. 137 

tional to the qua7itity of eUctricity that passes through it^ 
— that is to say, is proportional to the strength of the 
current while it passes, 

OviQ coulomb^ of electricity in passing through tne cell 
liberates -g-^l-^j:^ (or -000010352) of a gramme of hydro- 
gen, and causes ^%%l(^ (or -00033644) of a gramme of 
zinc to dissolve in the acid. 

II. TTie amotmt of chemical action is equal in each cell 
of a battery consisting of cells joined in series. 

The first of these laws was thought by Faraday, who 
discovered it, to disprove Volta's contact theory. He 
foresaw that the principle of the conservation of energy 
would preclude a mere contact force from furnishing a 
continuous supply of current, and hence ascribed the 
current to the chemical actions which were proportional 
in quantity to it. How the views of Volta and Faraday 
are ta be harmonised has been indicated in the last 
paragraph of Art. 72. 

Lesson XV. — Voltaic Batteries, 

167. A good Voltaic Battery should fulfil all or most 
of the following conditions : — 

1. Its electromotive-force should be high and con- 

stant. 

2. Its internal resistance should be small. 

3. It should give a constant current, and therefore 

must be free from polarisation, and not liable 
to rapid exhaustion, requiring frequent renewal 
•of the acid. 

4. It should be perfectly quiescent when the circuit 

is open. 

5. It should be cheap and ol durable materials. 

6. It should be manageable, and if possible, should 

not emit corrosive fumes. 

1 For the definition of the coulomhy or practical unit of quanUii (A 
electricity, see Art 323* 



138 ELEMENTARY LESSONS ON [chap. hi. 

168. No single battery fulfils all these conditions, 
however, and some batteries are better for one purpose 
and some for another. Thus, for telegraphing through 
a long line of wire a considerable internal resistance in 
the battery is no great disadvantage ; while, for producing 
an electric light, much internal resistance is absolutely 
fatal. The electromotive-force of a battery depends oo 
the materials of the cell, and on the number of cells 
linked together, and a high E.M.F. can therefore be 
gained by choosing the right substances and by taking 
a large number of cells. The resistance within the cell 
can be diminished by increasing the size of the plates, 
by bringing them near together, so that the thickness 
of the liquid between them may be as small as possible, 
and by choosing liquids that are ^ood conductors. Of 
the innumerable forms of battery that have been invented, 
only those of first importance can be described. Batteries 
may be classified into two groups, according as they 
contain one or two fluids, or electrolytes. 



Single-Fluid Cells. 

169. The simple cell of Volta, with its zinc and copper plates, 
has been already described. Cruickshank suggested to place 
the plates vertically in a trough, producing a more powerful 
combination. Dr. Wollaston proposed to use a plate of copper 
of double size, bent round so as to approach the tine on both 
sides, thus diminishing the resistance. Smee, as we have seen, 
replaced the copper plate by platinised silver, and Walker 
suggested the use of plates of hard carbon instead of copper or 
silver, thereby saving cost, and at the same time increasing the 
electromotive -force. The simple bichromate cell (Fig. 72) is 
almost the only single-fluid cell free from polarisation, and even 
in this form the strength of the current falls off *after a few 
minutes' working, owing to the chemical reduction of the liquid* 
Pabst used an iron-carbon cell with perchloride of iron as the 
exciting liquid. The iron dissolves and chlorine is at first 
evolved ; but without polarisation ; the liquid regenerating itseli 



CHAr. III.] ELECTRICITY AND MAGNETISM. 



139 



by absorbing oxygen from the air. It is very constant, but oi 
low E.]\I.F. Complete depolarization is usually obtained by 
two-fluid cells, or by cells in which in addition to the one fluid 
there is a depolarising solid body, such as oxide of manganese, 
oxide of copper, or peroxide of lead, in contact with the carbon 
pole. Such cells do not really belong to the class of single-fluid 
cells, and they are considered in the next group in which there 
are two electrolytes. 

Two-Fluid Cells. 

170. Daniell's Battery. — Each cell or " element " 
of Daniell's Battery consists of an inner and an outer 
cell, divided by a porous partition 
to keep the separate liquids in 
the two cells from mixing. The 
outer cell (Fig. 73) is usually of 
copper, and serves also as a 
copper plate. Within it is placed 
a cylindrical cell of unglazed 
porous porcelain (a cell of parch- 
ment, or even of brown paper, 
will ansv/er), and in this is a 
rod of amalgamated zinc for the 
negati\e pole. The liquid in 
the inner cell is dilute sulphuric 
acid ; that in the outer cell is a saturated solution of 
sulphate of copper {'' blue vitriol "), some spare crystals 
of the same substance being contained in a perforated 
shelf at the top of the cell, in order that they may 
dissolve and replace that which is used up while the 
battery is in action. 

\Yhen the circuit is closed the zinc dissolves in the dilute 
acid, forming sulphate of zinc, and liberating hydrogen gas ; but 
this gas does w^/ appear in bubbles on the surface of the copper 
cell, for, since the inner cell is porous, the molecular actions 
(by which the freed atoms of hydrogen are, as e^^lained by 
Fig. 155, handed on through the acid) traverse the pores of the 
inner cell, and there, in the solution of sulphate of coDoer, the 





Fig- 73r 



£40 ELEMENTARY LESSONS ON [chap, iri 

hydrogen atoms are exchanged for copper atoms, the result 
being that pure copper, and not hydrogen gas, is deposited 
on the outer copper plate. Chemically these actions may be 
represented as taking place in two stages. 

Zn -^ lljj SO4 = Zn SO4 + H2 

Zinc and Sulphuric A-cid produce Sulphate of Zinc and Hydrogen. 
And then 

H2 f Cu SO4 = H2 SO4 + Cu. 

Hydrogen and Sulphate of Copper produce Sulphuric Acid and Copper 

The hydrogen is, as it were, translated electro-chemically into 
copper during the round of changes, and so while the zinc dis- 
solves away the copper grows, the dilute sulphuric acid gradually 
changing into sulphate of zinc, and the sulphate of copper into 
sulphuric acid. There is therefore no polarisation so long as 
the copper solution is saturated ; and the battery is very 
constant, though not so constant in all cases as Clark's standard 
cell described in Art. 177, owing to slight variations in the 
cleclromotive-force as the composition of the other fluid varies. 
When sulphuric acid diluted with twelve parts of water is used 
the E.M.F. is i-i8i (legal) volts. The E.M.F. is 1-047 volts 
when concentrated zinc sulphate is used; 2x7 volts \'].cn 
a half-concentrated solution of zinc sulphate is used ; and, in 
the common cells made up with water or dilute acid, i -028 
volts or less. Owing to its constancy, this battery, made 
up in a convenient Hat form (Fig. 77)j ^^^ been much used 
\n telegraphy. 

171. Grove's Battery. — Sir Wm. Grove devised a 
iorm of batteiy having both greater E.M.F. and smaller 
internal resistance than DanielPs Cell. In Grove's 
element there is an outer cell of glazed ware or of 
ebonite, containing the amalgamated zinc plate and 
dilute sulphuric acid. In the inner porous cell a piece 
of platinum foil serves as the negative pole, and it dips 
into the strongest nitric acid. There is no polarisation 
in this cell, for the hydrogen liberated by the solution ol 
the zinc in dilute sulphuric acid, in passing through the 



CHAP. III. J ELECTRICITY AND MAGNETISM. 141' 

nitric acid in order to appear at the platintim pole, de- 
composes the nitric acid and is itself oxidized^ producing 
water ^nd the red fumes of nitric peroxide gas. This 
gas does/not, however, produce polarisation, for as it is 
very soluble in nitric acid it does not form a film upon 
the face of the platinum plate, nor does it, like hydrogen, 
set up an opposing electromotive -force with the zinc. 
The Grove cells may be made of a flat shape, the zinc 
being bent up so as to embrace the flat porous cell on 
both sides. This reduces the internal resistance, which 
is already small on account of the good conducting 
powers of nitric acid. Hence the Grove's cell will 
furnish for three or four hours continuously a powerful 
current. The E.M.F. of one cell is about 1*9 volts. A 
single cell will readily raise to a bright red heat two or 
three inches of thin platinum wire, or drive a small 
electro -magnetic engine. For producing larger effects 
a number of cells must be joined up '< in series," the 
platinum of one cell being clamped to the zinc of the 
next to it. Fifty such cells, each holding about a quart 
of liquid, amply suffice to produce an electric light, as 
will be explained in Lesson XXXII. 

172. Bunsen's Battery. — The! battery which bears 
Bunsen's name is a modification of that of Grove, and 
was indeed originally suggested by him. In the Bunsen 
cell the expensive ^'platinum foil is replaced by a rod or 
slab of hard gas carbon. The difficulty of cutting this 
into thin slabs causes a cylindrical form of battery, with 
a rod of carbon, as shown in Fig. 74, to be preferred to 
the flat form. The difference of potentials for a zinc- 
carbon combination is a little higher than for a zinc- 
platinum one, which is an advantage ; but the Bunsen 
cell is troublesome to keep in order, and there is some 
difficulty in making a good contact between the rough 

i Platinum costs about 7 dollars an ounce — nearly half as much as gold j 
whfle a hundredweight of the gas carbon may be had for a mere trifle, often 
for nothing more than the cost of carrying it ^om the gasworks. 



142 



ELEMENTARY LESSONS ON [chap. hi. 



surface of the carbon and the copper strap which 
connects the carbon of one cell to the zinc of the next. 
Fig. 75 shows the usual way of 
coupling up a series of five such 
cells. The Bunsen's battery will 
continue to furnish a current for 
a longer time than the flat 
Grove's cells, on account of the 
larger quantity of acid contained 
by the cylindrical pots.^ 

173. Leclanche*s Battery : 
Niaudet's Battel^. — For work- 
ing electric bells and telephones, 
and also to a limited extent in 
telegraphy, a zinc-carbon cell is 
employed, invented by Mons, 
the exciting liquid is not dilute 
In this the zinc 




•74. 



Leclanchd, in whicJi 
acid, but a solution of salammoniac. 
dissolves, forming a double chloride of zinc and am- 
monia, while ammonia _gas and hydrogen are liberated 




Fig. 75. 

at the carbon pole. To prevent polarisation the carbon 
plate is packed inside a porous pot along with frag- 

1 Callan constructed a large "battery in which cast-iron formed the positive 
pole, being immersed in strong nitric acid, the zincs dipping into dilute acid. 
The iron under these circumstances is not acted upon by the acid, but 
assumes a so-called "passive .state." In this condition its surface appears 
to be impreo^nated with a film of magnetic peroxide, or of oxygen. 



CHAP.JII.1 ELECTRICITY AND MAGNETISM. 



143 



ments of carbon and powdered binoxide of manga- 
nese, a substance which slowly yields up oxygen and 
destroys the hydrogen bubbles. If used to give a 
continuous current for many minutes together,, the 
power of the cell falls off owing to the accumulation of 
the hydrogen bubbles ; but if left to itself for a time the 
cell recovers itself, the binoxide gradually destroying the 
polarisation. As the cell is in other respects perfectly 
constant, and does not require renewing for months or 
years, it is well adapted for domestic purposes. Three 
Leclanch^ cells are shown joined in series, in Fig. 76. 




Fig. ']^. 

In more recent forms the binoxide of manganese is 
applied in a conglomerate attached to the face of the 
carbon, thus avoiding the necessity of using a porous 
inner cell. 

Mens. Niaudet has also constructed a zinc -carbon cell in 
which the zinc ds placed in a solution of common salt (chloride 
of sodium), and the carbon is surrounded by the so-called 
chloride-of-lime (or bleaching-powder), which readily gives up 
chlorine and oxygen, both of which substances will destroy the 
hydrogen bubbles and prevent polarisation. This cell has a 
higher E.M.F. and a less resistance than the Leclanche. De 
Lalande and Chaperon propose a cell in which oxide of copper 
i3 used as a solid depolariser in a solution of caustic potash. 

174. De la Rue's Battery. — Mr. De la Rue has 
constructed a perfectly constant cell in which zinc and 



144 ELEMENTARY LESSOI^S ON [chap, ill 

silver are the two metals, the zinc being immersed in 
chloride of zinc, and the silver embedded in a stick oi 
fused chloride of silver. As the zinc dissolves av/ay, 
metallic silver is deposited upon the -j- pole, just as the 
copper is in the Daniell's ceil. Mr. De la Rue has con- 
structed, an enormous battery of over ii,ooo little cells. 
The difference of potential between the first zinc and 
last silver of this gigantic battery was over i i,oo6 volts, 
yet even so no spark would jump from the + to the — 
pole until they were brought to within less than a quarter 
of an inch of one another. With 8040 cells the length 
of spark was only o-o8 of an inch. 

176. Mai'i^ Davy's Battery. — in this cell the zinc 
dips into sulphate of zinc, while a carbon plate dips into 
a pasty solution of mercurous sulphate. When the cell 
is in action mercury is deposited on the surface of the 
carbon, so that the cell is virtually a zinc-mercury cell. 
It was largely used for telegraphy in France before the 
introduction of the Leclanchd cell. 

176. Gravitation Batteries.— Instead of employ mg 
a porous cell to keep the two liquids separate, it is pos- 
sible, where one of the liquids is heavier than the other, 
to arrange that the heavier liquid shall form a stratum 
at the bottom of the cell, the lighter floating upon it. 
Such arrangements are called gravitation batteries; but 
the separation is never perfect, the heavy liquid slowly 
diffusing upwards. Daniell's cells arranged as gravi- 
tation batteries have been contrived by Meidinger, 
Minotto, Callaud, and Sir. W. Thomson. In Siemens' 
modification of Daniell's cell paper -pulp is used to 
separate the two liquids. The " Sawdust Battery " of 
Sir W. Thomson is a DanielPs battery, having the cells 
filled with sawdust, to prevent spilling and make them 
portable. 

177. Latimer Clark's Standard OelL — A standard 
cell whose E.M.F. is even more constant than that of 
the Daniell was suggested by Latirner Clark. This 



CHAP. III.] ELECTRICITY AND MAGNETISM. 



HS 



battery is composed of pure mercury, on which floats a 
paste of mercurous sulphate, a plate of zinc resting on 
the paste. Contact with the mercury, which acts as 
the positive pole, is made with a platinum wire. The 
E.M.F, is 1-436 legal volts. 

178. The following table gives the electromotive-forces 
of the various batteries enumerated : — 



Name of Battery, etc. 


E.M.F. in (legal) Volts. 


Single-Fluid Cells. 




Volta (Wollaston, etc.) 


1-036 — o-8i 


Smee -. . . . 


0*64 ? 


Poggendorff (Grenet, Trouvc 


'J 


etc.) . . . . 


2-27— 177 


Pabst . . . . 


078 


TwO'Fluid Cells. 




Daniell (Meidinger, Minotto 


) 


Thomson, etc.) 


I -122 — 1-07 — I '047 - 1-028 


Grove . . . . . 


J -934— 176 


Bunsen . 


1-942—173 


^ Leclanche 


1-59—1*46 — 1-402 


Niaudet . 


1-63 


Lalande and Chaperon 


0-66 


De la Rue 


I -046 


Marie Davy 


I'So 


Latimer Clark (Standard) 


1-436 


Secondary Batteries. 




Ritter 


2-22 — 1-47 


Plante (Faure, Sellon, etc.) 


2-22 — 1-96 



179. Strength of Current. — The student must not 
mistake the figures given in the above table for the 
strength of current which the various batteries vrlll 
yield; that depends, as was said in Lesson XIII., on 
the internal reststajtce of the cells as well as on their 
E.M.F. The E.M.F. of a cell is independent of its 
size, and is determined solely by the materials chosen 
and their condition. The resistance depends on the 

I. 



146 ELEMENTARY LESSONS ON [chap. hi. 

size of the cell, the conducting qualities of the liquid, 
the thickness of the liquid which the current must 
traverse, etc. 

The exact definition of the strength of a current is 
as follows : T/ie strength of a current is the qtcajidty oj 
electricity ivhich flows past any point of the circuit in 07ie 
second} Suppose that during lo seconds 25 coulombs 
of electricity flow through a circuit, then the average 
strength of that strong current during that time has been 
2\ coulombs per second, or 2| amperes. The usual 
strength of currents used in telegraphing over main 
lines is only from five to ten thousandths of an anipire. 

If in / seconds a quantity of electricity Q has flowed 
through the circuit, then the strength C of ^ the current 
during that time is represented by the equation : 

C.2. 

Moreover, if C represents the strength of the current, 
the total quantity of electricity that has passed through 
the circuit in a given time, t, is found by multiplying the 
strength of the current by tKe time ; or 

Q = c/. 

For the quantity of electricity that is thus transferred 
will be proportional to the strength, of the flow, and to 
the time that it continues. 

The laws which determine the strength of a current 
m a circuit were first enunciated by Dr. G. S. Ohm, who 
stated them in the following law» : 

180. Ohm*s La^w^. — 2" he strength of the current 
varies directly as the electromotive -force ^ and inversely 

1 The terms "strong," "great," and "intense," as applied to current^ 
mean precisely the same thing. Formerly, before Ohm's Law was properly 
understood, electricians used to talk about ''quantity currents," and 
** intensity currents," meaning by the former term a current flowing through 
a circuit in which there is very small resistance inside the battery or out ; 
^nd by the latter expression they designated a current due to a high electro- 
motive-force The terms were convenient, but should be avoided as mis- 
leading. 



CHAP. III.] ELECTRICITY AND MAGNETISM. 147 



as the resistance of the circMit ; or, in other words, any- 
thing that makes the E.M.F. of the cell greater will 
increase the strength of the current, while anything that 
increases the resistance (either the internal resistance in 
the cells themselves or the resistance of the external 
wires of the circuit) will dimmish the strength of the 
current. (See further concerning Ohm's Law in Lesson 
XXIX.) 

Now the internal resistances of the cells we have 
named differ very greatly, and differ with their size. 
Roughly speaking We may say that the resistance in a 
Daniell's cell is about five times that in a Grove's cell of 
equal size. The Grove's cell has therefore both a 
higher E.M.F. and less internal resistance. It would 
in fact send a current about eight times as strong as 
the DanielPs cell of equal size through a short stout 

wire. 

181. We may then increase the strength of a battery 

m two ways : — 

(1) by increasing its E.M.F 

(2) by diminishing its internal resistance. 

The electromotive. force of a cell being determined 
by the materials of which it is made, the only way to 




Fig. 77. 

increase the total E.M.F. of a battery of given materials 
IS to increase the number of cells joined in series. It is 



148 ELEMENTARY LESSONS ON [chap. iti. 

frequent in the telegraph service to link thus together 
two or three hundred of the flat DanielPs cells ; and 
they are usually made up in trough-like boxes, containing 
a series of lo cells, as shown in Fig. 77. 

To diminish the internal resistance of a cell the follow- 
mg expedients may be resorted to : — 

(i.) The plates may be brought nearer together, so 
that the current shall not have to traverse so thick a 
stratum of liquid. 

(2.) The size of the plates may be increased, as this 
affords the current, as it were, a greater number of 
possible paths through the stratum of liquid. 

(3.) The zincs of several cells may be joined together, 
to form, as it were, one large zinc plate, the coppers 
being also joined to form one large copper plate. Cells 
thus joined are said to be united " in parallel circuit," 
or " for quantity,'' to distinguish this method of joining 
from the joining in simple series. Suppose four similar 
cells thus joined, the current has four times the available 
number of paths by which it can traverse the liquid 
from zinc to copper ; hence the internal resistance of the 
whole will be only ^ of that of a single cell. But the 
E.M.F. of them will be no greater thus than that of 
one cell. 

It is most important for the student to remember that 
the strength of the current is also affected by the resist- 
ances of the wires of the external circuit ; and if the 
external resistance be already great, as in telegraphing 
through a long line, it is little use to diminish the internal 
resistance if this is already much smaller than the resist- 
ance of the line wire. 

The E.M.F. of the single-fluid cells of Volta and Smee 
IS marked as doubtful, for the opposing E.M.F. of polar- 
isation sets in almost before the true E.M.F. of the cell 
can be measured. The different values assigned to other 
cells are accounted for by the different degrees of con- 
centration of the liquids. Thus in the DanielPs cells 



CHAP. III.] ELECTRICITY AND MAGNETISM. 149 

used in telegrapny, water only is supplied at first in the 
cells containing the zincs ; and the E.M.F. of these is less 
than if acid or sulphate of zinc were added to the water. 

182. — Other Batteries. — Numerous other forms of battery 
have been suggested by different electricians. There are three, 
of theoretical interest only, in which the electromotive-foice is 
due, not to differences of potential at the contact of dissimilar 
metalsy but to differences of potential at the contact of a metal 
or metals with liquids. The first of these wa<? invented ]»y the 
Emperor Napoleon III. Both plates were of copper, dipping 
respectively into solutions of dilute sulphuric acid and of 
caustic soda, separated by a porous cell. The second of these 
coinbmations, due to Wohier, employs plates of aluminium only, 
dipping respectively into strong nitric acid and a solution of 
caustic soda. In the third, invented by Dr. Fleming, the two 
liquids do not even touch one another, being joined together by 
a second metal. In this case the liquids chosen are sodium 
persulphide and nitric acid, and the two metals copper and lead. 
A similar battery might be made with copper and zinc, using 
solutions of ordinary sodium sulphide, and dilute sulphuric acid 
in alternate cells, a bent zinc plate dipping into the first and 
second cells, a bent copper plate dipping into second and third, 
and so on ; for the electromotive - force of a copper - sodium 
sulphide-zinc combination is in the reverse direction to that of a 
copper-sulphuric acid-zinc combination. 

Bennett has lately described a cheap and most efficient battery, 
in which the metals are iron and zinc, and the exciting liquid a 
strong solution of caustic soda. Old meat-canisters packed with 
iron filings answer well for the positive element, and serve to 
contain the solution. Scrap zinc thro^vn into mercury in a 
shallow inner cup of porcelain forms the negative pole. 

Skrivanoff has modified the zinc-carbon cell of Latimer Clark^ 
by employing a stiff paste made of ammonio-mercuric chloride 
and common salt, thereby rendering the cells dry and portable. 

Jablochkoff has described a battery in which plates of carbon 
and iron are placed in fused nitre ; the carbon is here the 
electro-positive element, being rapidly consumed in the liquid. 

Planters and Faure's Secondary Batteries^ and Grove's 
Gas Battery^ are described in Arts. 415, 416. 

The so-called Dry Pile of Zamboni deserves notice. 
!t consists of a number of paper discs, coated with zinc- 



ISO ELEMENTARY LESSONS ON [chap, ill 

foil on one side and with binoxide of manganese on the 
other, piled upon one another, to the number of some 
thousands, in a glass tube. Its internal resistance is 
enormous, as the internal conductor is the moisture of 
the paper, and this is slight ; but its electromotive-force 
is very great, and a good dry pile will yield sparks. 
Many years may elapse before the zinc is completely 
oxidised or the manganese exhausted. In the Clarendon 
Laboratory at Oxford there is a dry pile, the poles of 
which are two metal bells : between them is hung a 
small brass ball, which, by oscillating to and fro, slowly 
discharges the .electricity. It has now been continuously 
ringing the bells for over sixty years. 

183. Effect of Heat on Batteriea — If a cell be 
warmed it yields a stronger current than when cold. 
This is chiefly due to the fact that the liquids conduct 
better when warm, the internal resistance bein^ thereby 
reduced. A slight change is also observed in the E.M.F. 
on heating ; thus the E.M.F. of a Daniell's cell is about 
J I per cent higher when warmed to the temperature of 
boiling water, while that of a bichromate battery falls oflf 
nearly 2 per cent under similar circumstances. 



Lesson XVI. — Magnetic Actions of the Current. 

184. About the year 1802 Romagnosi, of Trente, 
discovered that a voltaic pile affects a magnetised 
needle, and causes it to turn aside from its usual posi- 
tion. The discovery, ho^^ever, dropped into oblivion, 
having never been published. A connection of some 
kind between magnetism and electricity had long been 
suspected. Lightning had been known to magnetise 
knives and other objects of- steel; but almost all 
attempts to imitate these effects by powerful charges of 
electricity, or by sending currents of electricity through 



CHAP, ni.l ELECTRKITY AND iMAGNETISISI. 



iSJ 



steel bars, had failed.^ The true connection between 
magnetism and electricity remained to be discovered. 

In 1 8 19, Oerstedt, of Copenhagen, showed that a 
magnet tends to set itself at right-angles to a wire carry- 
ing an electric current. He also found that the way in 
which the needle turns, whether to the right or the left 
of its usual position, depends upon the position of the 
wire that carries the current — whether it is above or 
below the needle, — and on the direction in which the 
current flows through the wire. 

185. Oerstedt *s Experiment. — Veiy simple appar- 
atus suffices to repeat the fundamental experiment. Let 
a magnetic needle be suspended on a pointed pivot, as 
in Fig. 78. Above it, and parallel to it, is held a stout 




Fig. 78. 

copper wire, one end of which is joined to one pole of a 
battery of one or two cells. The other end of the wire 
is then brought into contact with the other pole of the 
battery. As soon as the circuit is completed the current 
flows through the wire and the needle turns briskly aside. 
If the current be flowing along the wire abo%fe the needle 

1 Down to this point in these lessons there has been no connection between 
magnetism and electricity, though something has been said about each. The 
student who cannot remember whether a charge of electricity does or does 
not affect a magnet, should turn back to what was said in Art 91. 



hS2 ELEMEl^TARY LESSONS ON [chap. jii. 

in the direction from north to south, it will cause the 
N.- seeking end of the needle to turn eastwards: if the 
current flows from south td north in the wire the N.-seek- 
ing end of the needle w;ll be deflected westwards. If 
the wire is, however, Mow the needle, the motions will 
be reversed, and a current flowing from north to south 
will cause the N. -seeking pole to turn westwards. 

186. Ampere's Rule. — To keep these movements 
in memory. Ampere suggested the following fanciful but 
useful rule. Suppose a man stemming in the wire with 
the^ ctirrent^ and that he turns so as to face the needle^ then 
the N. -seeking pole of the needle will be deflected towards 
his left hand. In other words, the deflection of the 
N. -seeking pole of a' magnetic needle, as viev/ed from 
the conductor, is towards the left of the current. 

For certain particular cases in which a fixed magnet pole acts 
on a movable circuit, the following converse to Amp^ris Rule 
will be found convenient. Suppose a man swimming in the 
wire with the current, ^and that he turns so as to look along the 
direction of the lines of force of the pole {Le. as the lines of 
fo2^ce run, from the pole if it be N. -seeking, towards the pole if it 
be S. -seeking), then he and the conducting wire with him v/ill be 
urged toward his left, 

187. A little consideration will show that if a current 

be carried below a needle in one direc- 
tion, and then back in the opposite 
direction aiove the needle, by bending 
the wire round, as in Fig. 79, the 
forces "exerted on the needle by both 
portions of the current will be in the 
same direction. For let a be the 
N.-seeking, and^the S.-seeking, pole 
of the suspended needle, then the 
Fig. 79. tendency of the ^current in the lower 

part of the wire will be to turn the 
needle so that a comes towards the observer, while b 




CHAP. in.J ELECTRICITY AND MAGNETISM. 153 

retreats ; while the current flowing above, which also 
deflects the N.-seeking pole to its left, will equally urge 
a towards the observer, and b from him. The needle 
v/ill not stand out completely at right-angles to the 
direction of the wire conductor, but v/ill take an oblique 
position. The directive forces of the earth's magnetism 
are tending to make the needle point north-and-south. 
The electric current is acting on the needle, tending 
to ma:ke it set .itself west -and -east. The resultant 
force will -be in an oblique direction between these,, 
and-will depend upon the relative strength of the two 
conflictir'^ forces. If the current is very strong the 
needle will turn widely round ; but could only turn com- 
pletely to a right-angle if the current, were infinitely strong 
If, however, the current is feeble in comparison \vith the 
directive magnetic force, the needle will turn very little. 
188. This arrangement will, therefore, serve roughly 
as iLGalvanoscope or indicator of currents; for the 
movement of the needle shows the direction of the 
current, and indicates whether it is a strong or a weak 
one. This apparatus is too rough to detect very delicate 
currents. To, obtain a more sensitive instrument there 
^re '^wo possible courses: (/.) Increase the effective 
attion of the current by carr^nng the wire more than 
once ,round the needle : (//.) Decrease the opposing 
directive force of the. earth's magnetism by some com* 
pensating contriva;ice. 

169*. Scli"weigger*s Multiplier. — The first of the 
above suggestions was carried out by Schweigger, who 
constructed a intiltiplier of many turns of v/ire. A suit- 
able 'frame 'of wood,, brass, or ebonite, is prepared to 
receive the wire, which must be " insulated," or covered 
with silk, or cotton, or guttapercha, to prevent the 
separate* turns of the coil from coming into contact with 
each other. Within this frame, which may be circular, 
e^Tliptical, or more usually rectangular, as in Fig. 80, the 
Needle is suspended, the frame being placed so that the 



154 ELEMENTARY LESSONG 0^ tCHAP. iii. 




wires lie in the magnetic meridian. The greater the 

number of turns the more 
powerful will be the mag- 
netic deflection produced 
by the passage of equal 
quantities of current. But 
if the wire is thin, or the 
number of turns of wire 
numerous, the resistance 
thereby offered to the flow 
of electricity may very 
greatly reduce the strength 
of the current. The student 
^^* ^' will grasp the importance 

of this observation when he has read the chapter on 
Ohth's Law. 

190. Astatic Oombinations. — The directive force 
exercised by the earth's magnetism on a magnetic needle 
may be -reduced or obviated by one of two methods : — 

(a.) By employing a. comj^msa^m^^ magnet An ordinary 
long bar magnet laid in the magnetic meridian, but with 
its N.- seeking pole' directed towards the. north, will, if 
placed horizontally above or below a suspended magnetic 
needle, tend to make the needle set itself with its S.-seek- 
ing pole north v/ards. If near the needle it may over- 
power the directive force of the earth, and cause the 
needle to reverse its usual position. If it is far away, all 
it can do is to lessen the directive force pf the earth. 
At a certain distance the magnet will, just compensate 
this force, and the needle will be neutral. This arrange- 
ment for reducing the earth's directive force is applied 
in the reflecting galvanometer shown in Fig. 91, in 
which the magnet at the top, curved in form and capable 
of adjustment to any height, affords a means of adjust- 
ing the instrument to the desired degree of sensitiveness 
by raising or lowering it. 

(^.) By using an astatic pair of magnetic needles. 



CHAP. III.] ELECTRICITY AND ivrAGNETISM. 



^SS 



Fig. 8i. 



If two magnetised needles of equal strength and size are 

bound together by a light wire of brass, or aluminium, 

in reversed positions, as 

shown in Fig. 8i, the force 

urging one to set itself in 

the magnetic meridian is 

exactly counterbalanced by 

the force that acts on the 

other. Consequently this 

pair of needles will remain 

in any position in which it is 

set, and is independent of the 

earth's magnetism. Such a 

combination is known as an 

astatic pair. It is, however, difficult in practice to 

obtain a perfectly astatic pair, since it is not easy to 

magnetise two needles exactly to equal strength, nor is 

it easy to fix them perfectly parallel to one another. 
Such an astatic pair is, however, 
readily deflected by a current flowing 
in a wire coiled around one of the 
needles ; for, as shown in Fig. 82, 
the current which flows above one 
needle and below the other will urge 
both in the same direction, because 
they are already in reversed positions. 
It is even possible to go farther, and 
to carry the wire round both needles, 
winding the coil around the upper in 
sense to that in which the coil is wound 



v/1 




the opposite 

round the lower needle. 

Nobili applied the astatic arrangement of needles to 
the multiplying coils of Schweigger, and thus constructed 
a very sensitive instrument, the Astatic Galvanoinete7% 
Shown Ln Fig. 88. The special forms of galvanometer 
adapted for the measurement of currents are described 
in the next Lesson. 



156 ELEMENTARY LESSONS ON [cHAt^. in 



191. Magnetic field due to OuiTeut. — Arago 
found that if a current be passed through a piece of copper 
wire it becomes capable of attracting iron filings to it 
so long as the current flows. These filings set them- 
selves at right angles to the wire, and cling around it, 
but drop off when the circuit is broken. There is, then, 
a magnetic '^ field," around the wire which carries the 
current ; and it is important to know how the lines of 
force are distributed in this field. 

Lfet the central spot in Fig. 83 represent an imaginary 
cross-section of the ware, and let us suppose tlie current 
to be flowing in through the paper at that point. Then 
by Ampere's rule a magnet needle placed below will.tend 
to set itself in the position showai, with its N. pole 
pointing to the left.^ The current will urge a needle 
above the w^lre into the reverse position, A needle on 
the right of the current will set itself at right angles to 
the current (/.^. in the plane of the paper), and with its 

N. pole pointing down^ 
g^ ^^ — ? while the N. pole of a 

^4 / \ needle on the left would 






/ 




be urged up. In fact the 
tendency w^ould be to urge 
the .N. pole round the 

Fig. w3. Fig. 84. J ^ • ^t. 

^ conductor m the same 

way as the nands of a watch niove ; while the S. pole 
would be urged in the opposite cyclic direction to that of 
the hands of a watch. If the cun*ent is reversed, and is 
regarded as flowing to\vards the^ reader, i.e. comi»g up 
cut of the plane of the paper, as in the diagram of Fig. 

1 If the student has any difficulty in applying Ampere's rule to this case and 
the others which succeed, he should carefully follow out the follbwing mental 
operation. Consider the spot marked *' ht " as a hole in the ground into 
which the current is flowing, and into which he dives head-foremost. While 
in the hole he must turn round so as to face each of the magnets in succession, 
and remember that in each case the N. -seeking pole will be urged to ^w left 
In diagram 84 he must conceive himself as coming up out of the hole m the 
ground where the current is flowing out. 



CHAP. III.] ELECTRICITY AND MAGNETISM. 157 



84, then the motions would be just in the reverse sense. 
It would seem from this as if a N. -seeking pole of a 
magnet ought to revolve continuously round and round a 
current ; but as we cannot obtain a magnet with one 
pole only, and as the S. -seeking pole is urged in an 
opposite direction, all that occurs is that the needle sets 
itself as a tangent to a circular curve surrounding the 
conductor. This is what Oerstedt meant when he 
described the electric current as acting ** in a revolving 
manner," upon the magnetic needle. The field of force 
with its circular lines surrounding 
a current flowing in a straight 
conductor, can be examined ex- 
perimentally with iron filings in 
the following way : A card is 
placed horizontally and a stout 
copper wire is passed vertically 
through a hole in it (Fig. 85). 
Iron filings are sifted over the 
card (as described in Art. 108), 

Fig. 85. 

and a strong current from three 

or four large cells is passed through the wire. On 
tapping the card gently the filings near the wire set 
themselves in concentric circles round it. 

192. Equivalent Magnetic Shell: Ampere's 
Theorem. — For many purposes the following way of 
regarding the magnetic action of electric currents is 
more convenient than the preceding. Suppose we take 
a battery and connect its terminals by a circuit of wire, 
and that a portion of the circuit be twisted, as in Fig. 86, 
into a looped curve, it. will be found that the entire 
space enclosed by the loop possesses magnetic properties. 
In our figure the current is supposed to be flowing round 
the loop, as viewed from above, in the same direction as 
the hands of a clock move round ; an imaginary man 
swimming round the circuit and always facing towards 
the centre would have his left side down. By Ampere's 




I5S 



ELEMENTARY LESSONS ON [chap. in. 



rule, then, a N. pole would be urged downwards through 
the loop, while a S. pole would be urged upwards. In 
fact the space enclosed by, the loop of the circuit behaves 




Fig. 86. 

like a magnetic shell (seg'Art. 107), having its upper face 
of S.-seekirig magnetism, and its lower face of N. -seeking 
magnetism. It can be shown in every case that a closed 
voltaic circuit is equivalent to a inag7ietic shell whose 
edges coincide in position with the circuity the shell being 
of such a strength that the number of its. lines offeree is 
the same as that of the lines of force due to the current 
in the circuit. The circuit acts on a magnet attracting 
or repelling it, and being attracted or repelled by it, just 
exactly as its equivalent magnetic shell would do. Also, 
the circuit itself, when placed in a magnetic field, experi- 
ences the. same force as its equivalent magnetic shell 
would do. 

193. Maxwell's Rule. — Professor Clerk Maxwell, 
who developed this method of treating the subject, has 
given the following elegant rule for determining the 
mutual action of a circuit and a magnet placed near it. 
Every portion of the circuit is acted upon by a force 
urging it in such a direction as to make it enclose 
within its embrace the greatest possible mmiber of lines of 



:hap. III.] ELECTRICITY AND MAGNETISM. 



IS9 



force. If the circuit is fixed and the magnet movable, 
then the force acting on the magnet will also be such as to 
tend to make the number of lines of force that pass 
through the circuit a maximum (see also Art. 317). 

194. De la Rive's Floating Battery. — The pre- 
ceding remarks may be illustrated experimentally by 
the aid of a little floating battery. A plate of zinc and one 
of copper (see Fig. 87) are fixed side by side in a large 




Fig. 87. 

cork, and connected above by a coil of covered copper wire 
bent into a ring. This is floated upon a dish containing 
dilute sulphuric acid. If one pole of a bar magnet be 
held towards the ring it will be attracted or repelled 
according to the pole employed. The floating circuit 
will behave like the floating m^agnet in Fig. 44, except 
that here we have what is equivalent to a floating 
magnetic shell. If the S. pole of the magnet be pre- 
sented to that face of the ring which acts as a S. -seeking 
pole (viz. that face round which the current is flowing 



i6o ELEMENTARY LESSONS ON [chap, ni 

in a clockwise direction)/ it will repel it If the pole be 
thrust right into the ring, and then held still, the battery 
will be strongly repelled, will draw itself off, float away, 
turn round so as to present toward the S. pole of the 
magnet its N. -seeking face, will th.en be attracted up, 
and will thread itself on to the magnet up to the middle, 
in which position as many magnetic lines of force as 
possible cross the area of the ring. 

It can be shown also that two circuits traversed by 
currents attract and repel one another just as two 
magnetic shells would do. 

It will be explained in Lesson XX VL on Electro- 
magnets how a piece of iron/or steel can be magnetised 
by causing a current to flow in a spiral wire round it. 

195, Strength of the Ciirrent in Magnetic 
Measure, — When a current thus acts on a magnet pole 
near it, the force /which it exerts will be proportional 
to the strength / of the current, and proportional also 
to the strength 7n of the magnet pole, and to the length 
/ of the wire employed : it will -also vary inversely as 
the square of the distance r from the circuit to the 

magnet pole. Or, / = '-^ dynes. Suppose the wire 
looped up into a circle round the magnet pole, then 
/=27rr, and f=^— m dynes. Suppose also that the 

T 

Circle is of one centimetre i-adius, and that the magnet 
pole is of strength of one unit (see Art. 125), then the 

force exerted by the current ol strength / will be — x i, 

or 2TTi dynes. In order, therefore, that a current of 
strength i should exert a force of / dynes on the unit pole, 
one must consider the current as travelling round only -L. 

part of the circle, or round a portion of the circum- 
ference equal in length to the radius. 

196. Unit of Current Strength. — A current is 
$aid to have a strength of one ** absolute " unh when it 



CHAP. III.] ELECTRICITY AND MAGNETISM. i5! 

IS such that if one centhn^re length of the circuit is bent 
into an arc of one centimetre radius, the current in it 
exerts a force of one dyne on a magnet-pole of unit 
strength placed at the centre of the arc. The practical 
unit of " one ampere ** is only ro of this theoretical unit. 
{See also Art. Z'^Z-) 



Lesson XV 1 1 • — Galvanometers. 

197. The term Galvanometer is applied to an 
instrument for measuring the strength of electric 
currents by means of the deflection of a magnetic needle, 
round which the current is caused to flow through a coil 
of wire. The simple arrangement described in Art. i88 
was termed a '* Galvanoscope,'' or current indicator^ but 
it could not . rightly be termed a "galvanometer"^ or 
current measurer^ because its indications were only 
qualitative, not quantitative. The indications of the 
needle did not afford accurate knowledge as to the exact 
strength of current flowing through the instrument. A 
good galvanometer must fulfil the essential condition that 
its readings shall really measure the strength of the 
current in some certain way. It should also be suffici- 
ently sensitive for the currents that are to be measured 
to affect it. The galvanometer adapted for measuring 
very small currents (say a current of only one or two 
millionth parts of an ampere) will not be suitable for 
measuring very strong currents, such as are used in pro- 
tiucing an electric light. Moreover, if the current to be 
measured has already passed through a circuit of great 
resistance (as, for example, some miles of telegraph 
wire), a galvanometer whose coil is a short one, consist- 

1 The terms ** Rheoscope** and " Rheometer^'' are still occasionally applied 
lo these instruments. A current interrupter is sometimes called a ** Rheo- 
iovt^^*^ and the Commutator or Current Reverser, shown in Fig. 149, is 
»n some books called a " Rheotrop^ ; but there terms are dropping out of use. 

M 



l62 



ELEMENTARY LESSONS ON [chap. hi. 



ing only of a few turns of vvire, will be of no use, and a 
long-coil galvanometer must be employed with many 
turns of wire round the needle. The reason of this is, 
explained hereafter (Art. 352). Hence it will be seen 
that different styles of instrument are needed for different 
kinds of work ; but of all the requisites are that they 
should afford quantitative m.easurements, and. that they 
should be sufficiently sensitive for the current that is to 
be measured. 

198. Nobili*s Astatic Galvanometer. — The 
instrument constructed by Nobili, consisting of an astatic 
pair of needles delicately hung, 30 that the lower one lay 

within a coil of wire 




Fig. 88. 



wound upon an ivory 
frame (Fig. 88), was 
for long the favourite 
form of sensitive 
galvanometer. The 
needles of this instru- 
ment^ being indepen- 
dent of the earth's 
magnetism, take their 
position in obedience 
to the torsion of the 
fibre by which they 
are hung. The frame 
on which the coil is 
wound must be set 
carefally parallel to 



the needles ; and three screw feet serve to adjust the 
base of the instrument level. Protection against cur- 
rents of air is afforded by a glass shade. When a 
current is sent through the wire coils the needles move 
to right or left over a graduated circle. When the 
deflections are sinall (i.e. less than 10"^ or ) 5°), they are 
very nearly proportional to the strength of the currents 
that produce them. Thus, if a current produces a 



CHAP. III.] ELECTRICITY AND MAGNETISM. 163 

deflection of 6° it is known to be approximately three 
times as strong as a current which only turns the needle 
through 2**. But this approximate proportion ceases to 
be true if the deflection is more than 15° or 20°; for 
then the needle is not acted upon so advantageously by 
the current, since the poles are no longer within the coils, 
but are protruding at the side, and, moreover, the needle 
being oblique to the force acting on it, part only of the 
force is turning it against the directive, force of the fibre ; 
the other part of the force is uselessly pulling or pushing 
the needle along its length. It is, however, possible to 
" calibrate " the galvanometer, — that is, to ascertain by 
special measurements, or by comparison with a standard 
instrument, to what strengths of current particular 
amounts of deflection correspond. Thus, suppose it once 
known that a deflection of 32° on a particular galvano- 
meter is produced by a current of t-J-it of an ampere, then 
a current of that strength will always produce on that 
mstrument the same deflection, unless from any accident 
the torsion force or the intensity of the magnetic field is 
altered. 

199. The Tang'ent Galvanometer. — It is not— 
for the reasons mentioned above — possible to construct 
a galvanometer in which the a^igle (as measured in 
degrees of arc) through which the needle is deflected is 
proportional throughout its whole range to the strength 
of the current. But it is possible to construct a very 
simple galvanometer in which the tangent'^ of the angle 
of deflection shall be accurately proportional to the 
strength of the current. Fig. 89 shows a frequent form 
of Tangent Galvanometer. The coil of this instru- 
ment consists of a simple circle of stout copper wire 
from ten to fifteen inches in diameter. At the centre is 
delicately suspended a magnetised steel needle not 
exceeding one inch in length, and usually furnished with 
a light index of aluminium. The instrument is adjusted 

1 See note on Ways jf Reckoning Angles, p. 109. 



564 



ELEMENTARY LESSONS ON [chap. hi. 



by setting the coil in the magnetic meridian, the small 
needle lying then in the plane of the coil. One essential 
feature of this arrangement is, that while the coil is very 
large, the needle is relatively very small. The " field " 




Fig. 89. 

due to a current passing round the circle is very uniform 
at and near the centre, and the lines of force are there 
truly normal to the plane of the coil.^ This is not true 
of other parts of the space inside the ring, the force 
being neither uniform nor normal in directi-on, except zn 
the plane of the coil and af its centre- The needle being 

1 In order to ensure uniformity of field, Gaugam proposed to hang the 
needle at a point on the axis of the coil distant from its centre by a distance 
equal to half the radius of the coils. Helmholtzs arrangement of two 
parallel coils, symmetrically set on either side of the needle, is better ; and a 
three-coil galvanometer having the central coil larger than the others, so that 
all three may lie in the surface of a sphere having the small needle at its 
centre, is the best arrangement of all for ensuring that the field at the centre 
is uniform. 



CHAP. III.] ELECTRICITY AND MAGNETISM. 165 

small its poles are never far from the centre, and hence 
never protrude into the regions where the magnetic force 
is irregular. Whatever magnetic force the current in 
the coil can exert on the needle is exerted normally to 
the plane of tEe ring, and therefore at right angles to 
the magnetic meridian. Now, it was proved in Art. 124 
that the magnetic force which, acting at right angles to 
the meridian, produces on a magnetic needle the de- 
flection S is equal to the horizontal force of the earth's 
magnetism at that place multiplied by the tangent of the 
angle of deflection. Hence a current flowing in the coil 
will turn the needle aside through an angle such that the 
tangent of the angle of deflection is proportional to the 
strength of the current. 

Example. — Suppose a certain battery gave a deflection of 
15* on a tangent galvanometer, and another battery 
yielding a stronger current gave a deflection of 30°. The 
strengths currents are not in the proportion of 15 : 30, 
but in the proportion of tan i s"* to tan 30"^. These 
values must be obtained from a Table of natural tangents 
like that given on p. iii, from which it will be seen 
that the ratio between the strengths of the currents is 
•268 : '577, or about 10 : 22. 

Or> more generally, if current C produces deflection 5, and 
* .current C deflection h\ then 

C :C' = tan 5 : tan 5' 

To obviate reference to a table of figures, the circular 
scale of the instrument is sometimes graduated into 
tasigent values instead of being divided into equal 
degrees of arc. Let a tangent O T be drawn to the 
circle, as in Fig. 90, and along this line let any number 
of equal divisions be set off, beginning at O. From 
these points draw back to the centre. The circle ^will 
thus be divided into a number of pieces, of which those 
near O are nearly equal, but which get smaller and 
smaller away from O. These unequal pieces correspond 



i66 



ELEMENTARY LESSONS ON [chap. in. 



to equal increments of the tangent. If the scale were 
divided thus, the readings would be proportional to 
the tangents. It is, however, harder to divide an arc 




Fig. 90. 

into tangent-lines with accuracy than to divide it into 
equal degrees ; hence this graduation, though convenient, 
is not used where great accuracy is needed. 

200. Absolute Measure of Current by Tangent Gal* 
vanometer. — The strength of a current may be determined in 
" absolute " units by the aid of the tangent galvanometer if the 
*' constants " of the instrument are knov/n. The tangent of the 
angle of deflection represents {see Art. 124) the ratio between 
the magnetic force due to the current and the horizontal com- 
ponent of the earth's magnetic force. Both these forces act on 
the needle, and depend equally M^on the magnetic moment of the 
needle, which, therefore, we need not know for this purpose. 
We know that the force exerted by the current at centre of the 
coil is proportional to the horizontal force of the earth's mag 
netism multiplied by the tangent of the angle cf deflection. 
These two quantities can be found from the table:^, and from 
them we calculate the absolute value of th^ current, as follows : — 
Let r represent the radius of the galvaiKDmeter coil (measured in 
centimetres) ; its total length (if of one turn only) is 2irr. The 
distance from the centre to all parts of the coil is of course r. 
From our definition of the unit of strength of current (Art. 196), 

it follows that i x -o- ~ force (in dynes) at centre, 



or 



hence 



27r 
i X — = H ' tan 5 : 
r 



z ss 



2T 



' H • tan a. 



CHAP. III.] ELECTRICITY AND MAGNETISM. 167 



The quantity — is called the ** constant" of the galvanometer 

Hence we obtain the value of the current in absolute (electro- 
magnetic) units ^ by multiplying together the galvanometer con- 
stant, the horizontal magnetic force at the place, and the tangebt 
of the angle of deflection. Tangent galvanometers aie often 
made with more than one turn of wire. In this case the " con- 

stant " Is where n is the uumber of turns in the coil. 

200 {his). Am-meter. — Professors Ayrton and Perry have, also, desigrnpd 
seme galvanometers for electric-light work, intended to show by a pointer 
attached to the ma^etic needle the strength of the current in a7!ij[>h es {An 
323). In these instruments, which are portable, and "dead-beat" in action, 
the needle is placed between the poles of a powerful permanent magnet to 
control its direction and make it independent of the earth's magnetism. By 
a peculiar shaping of the pole-pieces, needle, and coils, the angular deflections 
are proportional to the strength of the deflecting current The coils are in 
ten sections, v/hich can be grouped either " in series '* or " in parallel ** at 
will, by turning an appropriate commutator, thus enabling the scale-readings 
to be verified by using one ordinary cell. These A m-meUrs are made with 
short-coils of very low resistance and few turns of wire. Ayrton and Perry 
have also arranged Volt7neters {see Art. 360 d)^ with long -coils of high re- 
sistance, in a similar way. 

201. Sine Galvanometer. — The disadvantage of 
the tangent galvanometer just described is that it is not 
very sensitive, because the coil is necessarily very large 
rs compared v^ith the needle, and therefore far away 
from it. A galvanometer with a smaller coil or a larger 
needle could not be used a:, a tangent galvanometer, 
though it w^ould be more sensitive. Ajty sensitive 
galvanometer in which the needle is directed by the 
earth's magnetism can, however, be used as a Sine 
Galvanometer, provided the frame on which the coils 
are wound is capable of being turned round a central 
axis. When the instrument is so constructed, the 
follov/ing method of measuring currents is adopted. 
The coils are first set parallel to the needle {i.e, in the 
magnetic meridian) ; the current is then sent through 
it, producing a deflection ; the coil itself is rotated round 
in the same sense, and, if turned round through a wide 

1 The student will learn (Art. 196 and 323) that the practical unit of 

current which we call " one ainj>ere " is only i. of one ** absolute " unit of tae 

- 10 

centimetre -gramme -second system. 



i68 ELEMENTARY LESSONS ON [chap. in. 



enough' angle, will overtake the needle,' which' will once 
more lie parallel to the coil. In this position two forces 
are acting on the needle : the directive force of the 
earth's magnetism acting along the magnetic meridian, 
and the force due to the current passing in the coil, 
which tends to thrust the poles of the needle out at 
right angles ; in Tact there is a "couple" which exactly 
balances the " couple " due to terrestrial magnetism. 
Now it was shown in the Lesson on the Laws of Mag- 
netic Force (Art. 123), that when a needle is deflected 
the " moment " of the couple is proportional to the sine 
of the angle of deflection. Hence in the sine galvano- 
meter, when the coil has been turned round so that the 
needle once more lies along it, the strength of the ctcrrent 
in the coil is proportional to the sine of the angle through 
which the coil has been turned, ^ 

202. The Mirror Galvanometer.— When a gal- 
vanometer of great delicacy is needed, the moving parts 
must be made very light and small. To watch the 
movements of a veiy small needle an index of some 
kind must be used ; indeed, in the tangent galvanometer 
it is usual to fasten to the short stout needle a delicate 
stiff pointer of aluminium. A far better method is to 
fasten to the needle a veiy light mirror of silvered glass, 
by means of which a beam of light can be reflected on 
to a scale, so that every slightest motion of the needle 
is magnified and made apparent. The mirror galvano- 

1 Again the student who aesires to compare the strength of two currents 
will require the help of a Table of natural sines, like that given on page iii. 
Suppose that with current C the coils had to be turned through an angle of 
f) degrees ; and that with a different cun-ent C the coils had to be turned 
through 0' degrees, then 

C : C = sin ^ : sin ff. 

It is gf course assumed that the instrument is provided with a scale of 
degrees on which to read off the angle through which the coils have been 
turned. It is possible here also, for rough purposes, to graduate the circle 
not in degrees of arc but in portions corresponding to equal additional 
values of the sine. The student should try this way of dividing a circle 
after ^reading the note On Wajrs^ofJReckoning Angles, p. log. 



CHAP. III.] ELECTRICITY AND MAGNETISM. 



169 



fneters devised by Sir. W. Thomson for signalling through 
submarine cables, are admirable examples of this class 
of instrument. In Fig. 91 the general arrangements of 
this instrument are shown. The body of the galvano- 
meter is supported on three screw feet by which it can 
be adjusted. The magnet consists of one or more 
small pieces of steel watch-spring attached to the back 




Fig. 91 

of a light concave silvered glass mirror about as large 
as a ten cent piece. This mirror is hung by a single 
fibre of cocoon silk within the coil, and a curved magnet, 
which serves to counteract the magnetism of the earth, 
or to direct the needle, is carried upon a vertical support 
above. Opposite the galvanometer is placed the scale. 
A beam of light from a paraffin lamp passes through 
a narroy/ aperture under the scale and falls on the 
mirror, which reflects it back on to the scale. The 
mirror is slightly concave, and gives a v/ell defined spot 
of light if the scale is adjusted to suit the focus cf the 



I70 ELEMENTARY LESSONS ON [chap. in. 

mirror/ The adjusting magnet enables the operator to 
bring the reflected spot of light to the zero point at the 
middle of the scale. The feeblest current passing through 
the galvanometer will cause the spot of light to shift to 
right or left. The tiny current generated by dipping 
into a drop of salt water the tip of a brass pin and a 
steel needle (connected by wires to the terminals of the 
galvanometer) will send the spot of light swinging right 
across the scale. If a powerful lime -light is used, the 
movement of the needle can be shown to a thousand 
persons at once. For still more delicate work an astatic 
pair of needles can be used, each being surrounded by 
its coil, and having the mirror rigidly attached to one of 
the needles. 

Strong currents must not be passed through very 
sensitive galvanometers, for, even if they are not spoiled, 
the deflections of the needle will be too large to give 
accurate measurements. In such cases the galvan- 
om^^r is used with a shunt^ or coil of wire arranged so 
that the greater part of the current shall flow through it, 
and pass the galvanometer by, only a small portion of the 
current actually traversing the coils of the instrument. 
The resistance of the shunt must bear a known ratio to 
the resistance of the instrument, according to the prin- 
ciple laid down in Art. 353 about branched circuits. 

203. Differential Galvanometer. — For the pur- 
pose of comparing two currents a galvanometer is 
sometimes employed, in which the coil consists of two 
separate wires wound side by side. If two equal currents 
r.re sent in opposite directions through these wires, the 
rxedle will not move. If ths currents are, however, 
unequal, then the needle will be moved by the stronger 

1 As concave mirrors are expensive, a plain mirror behind a lens cf 
suitable focus may be substituted. The thin discs of glass used in 
mounting objects for the microscope form, when silvered, excellent light 
mirrors. Where great accuracy is desired a fine wire is placed in the 
aperture traversed by the beam of light, and the image of this appears 
when focused on the screen as a dark line crossing the spot of light. 



CHAP, iii.j ELECTRICITY AND MAGNETISM. 171 

of them, with an intensity corresponding to the difference 
of the strengths of the two currents 

204. Ballistic Q-alvanometer. — In order to measure 
the strength of currents which last only a very short time, 
galvanometers are employed in which the needle takes 
a relatively long time to swing. Xbis is the case with 
long or heavy needles ; or the needles may be weighted 
by enclosing them in leaden cases. As the needle swirls 
slowly round, it adds up, as it were, the Varying impulses 
received during the passage of a transient current. 
The sine 0/ half the angle of the first swing is proportional 
to the qtiantity of electricity that has flowed through the 
coil. The charge of a condenser may thus be measured 
by discharging it through a ballistic galvanometer. 

Lesson XVIII. — Che7nical Actions of the Current : — 

Voltameters. 

205. In addition to the chemical actions inside the 
cells of the battery, which always accompany the produc- 
tion of a current, there are also chemical actions produced 
outside the battery when the current is caused to pass 
through certain liquids. Liquids may be divided into 
three classes — (i) those which do not cojidtcct at all^ such 
as turpentine and many oils, particularly petroleum ; (2} 
those which co7idtcct without decomposition^ viz. mercury 
and other molten metals, which conduct just as solid 
metals do ; (3) those which are decoinposed when they 
conduct a cm-rent^ viz. the dilute acids, solutions of 
metallic salts, and certain fused solid compounds. 

206. Decomposition of "Water. — In the year 1 800 
Carlisle and Nicholson discovered that the voltaic current 
could be passed through water, and that in passing through 
it decomposed a portion of the liquid into its constituent 
gases. These gases appeared in bubbles on the ends of 
the wires which led the current into and out of the 
iiquid ; bubbles of oxygen gas appearing at the point 



172 ELEMENTARY LESSONS ON [chap. ill. 

where the current entered the liquid, and hydrogen 
b^ibbles where it left the liquid. It was soon found that 
a great many other liquids, particularly dilute acids and 
solutions of metallic salts, could .be sinlilarly decomposed 
by passing a current through them. 

207. Electrolysis. — To this, process of decomposing 
a liquid by means of an electric current Faraday gave 
the name of electrolysis (/.<?. electric analysis) ; and 
those substances- which are/capable of being thus decom- 
posed or '' electrolysed " he termed electrolytes. 

The ends of the wires leading from and to the battery 
are called electrodes ; and to distinguish them, that by 
which the current enters is called the anode, that by 
which it leaves the kathode. The vessel in which a 
liquid is placed for electrolysis is termed ^.n electrolytic cell, 

208. Electrolysis of Water. — Returning to the 
decomposition of water, we may remark that perfectly 
pure water apjpears not to conduct, but its resistance is 
greatly reduced by the addition of a few drops of sul- 
phuric or of hydrochloric acid. The apparatus shown in 
Fig. 92 is suitable for this purpose. Here a battery of 
two cells (those shown are circular Bunsen's batteries) 
is seen with its poles connected to two strips of metallic 
platinum as electrodes, which project up into a vessel con- 
taining the acidulated water. Two tubes closed at one 
end, which have been previously filled with water and 
inverted, receive the gases evolved at the electrodes. 
Platinum is preferred to other metals such as copper or 
iron for electrodes, since it is less oxidisable and resists 
every acid. It is found that there is almost exactly 
twice as much hydrogen gas (by volume) evolved at the 
kathode as there is of oxygen at the anode. This fact 
corresponds with the known chemical composition of 
water, which is produced by combining together these 
two gases in the proportion of two volumes of the 
former to one of the latter. The proportions of gases 
evolyed, however, are not exactly two to one, for at first a. 



CHAP. III.] ELECTRICITY AI^ID MAGNETISM. 



173 



very small quantity of the hydrogen is absorbed or 
" occluded " by the platinum surface, while a more con- 
siderable proportion of the oxygen — about i per cent— 




Fig. 92. 

is given off in the denser allotropic form of ozone^ which 
occupies less space and is also slightly soluble in the 
water. When a sufficient amount of the gases has been 
evolved and collected they may be tested ; the hydrogen 
by showing that it will burn, the oxygen by its causing 
a glowing spark on the end of a 'splinter of wood to burst 
into flame. If the two gases are collected together in a 
common receiver, the mixed gas will be found to possess 
the well knowii explosive property of mixed hydrogen 
and oxygen gases. The chemical decomposition is ex- 
pressed in the following equation : 
H,0 = H, + O 

Water yields 2 vols, of Hydrogen and i vol. of Osygen. 

209. Electrolysis of Sulphate of Copper. --^We 

will take as another case the electrolysis of a solution of 
the well-known f«J)lue vitriol" or sulphate of copper. If 



174 ^ ELEMENTARY LESSONS ON fcHAP. rri, 

a few crystals of this substance are dissolved in watci 
a blue liquid is obtained, which is easily electrolysed 
between two electrodes of platinum foil, by the current 
from a single cell of any ordinary battery. The chemical 
formula for sulphate of copper is CuSO^. The result of 
the electrolysis is to split it up into metallic copper, 
which is deposited in a film upon the kathode, and 
" Sulphion " an easily decomposed compound of sulphur 
and oxygen, which is immediately acted upon by the 
water forming sulphuric acid and oxygen. This oxygen 
is liberated in bubbles at the anode. The chemical 
changes are thus expressed : 

CUSO4 = Cu + SO, 

Sulpliate of Copper becomes Copper and Sulphion ■, 

so, + H,0 = HjSO, + O 

Sulphion and water produce Sulphuric acid and Oxygen. 

In this way, as the current continues to flow, copper is 
• continually withdrawn from the liquid and deposited on 
the kathode, and the liquid gets more and more acid. If 
copper electrodes are used, instead of platinum, no oxygen 
is given off at the anode, but the copper anode itself dis- 
solves awa)' into the liquid at exactly the same rate as 
the copper of the liquid is deposited on the kathode. 

210. Anions and Kathions. — The atoms which 
thus are severed from one another and carried in\isibly 
by the current to the electrodes, and there deposited, 
are obviously of two classes : one set go to the anode, 
the other to the kathode. Faraday gave the name of 
ions to these wandering atoms ; those going to the 
anode being anions, and those going to the kathode 
being kathions. Anions are sometimes regarded as 
" electro-negative " because they move as if attracted 
toward the + pole of the battery, while the kathions 
are regarded as " electro-positive." Hydrogen and the 
metals are kathions, moving apparently za/Z/t the direction 
assumed as that of the current, and are deposited' where 



CHAP. III.] ELECTRICITY AND MAGNETISM. 175 

the current leaves the electrolytic cell. The anions are 
oxygen, chlorine, etc. When, for example, chloride oi 
tin is electrolysed, metallic tin is deposited on the kath- 
ode, and chlorine gas is evolved at the anode. 

211. Quantitative "Laws of Electrolysis. 

(1.) T/ie a7nounl oj chemical action is egiial at all poijtfs, 
of a circuil. If two or more electrolytic cells are placed 
at different points of a circuit the amount of chemical 
action will be the same in all, for the same qifantity of 
electricity ftows pasi every point of the circuit in the 
same time. If all these cells contain acidulated water, 
the quantity, for example, of hydrogen set free in each 
will be the same ; . or, if they contain a solution of 
sulphate of copper, identical quantities of copper will be 
deposited in each; If some of the cells contain acidu- 
lated water, and others contain ^ sulphate - of copper, the 
weights of hydrogen and of copper will. not- h^. equal, 
but will be in chemically egiiivale7ti quantities. 

(ii.) The anwimt 0/ an ion liberated at an^ electrode 
in a given lime Js proportional to the strength of the 
current, A current of 2 a^nperes will cause just twice 
the quantity of chemical decomposition to take place as 
a current of i ampere would do in the jsame time. 

(iii.) T}ie ammcnbof an ion liberated at an electrode 
in one second is equal to the strength of the current 
multiplied by the ^^ electro -chemical equivalent'''^ of the 
ion. It has been found by experiment that the passage 
of one coulomb of electricity through water liberates 
•000010352 gramme^ of hydrogen. Hence, a current 
the strength of which ^is C \amperes) will liberate C x 
•000010352 grammes of hydrogen per second. The 
quantity -000010352 is called the electro-chemical equiva- 
lent of hydrogen. The *Selectro-chemical equivalents" 
of other elements can be easily calculated if their 
chemical "equivalent" is known. Thus the chemical 

1 Lord Rayleigh says '000010352 ; Ma.scart, '000010415 ; F. and W. Kohl 
rausch, •.000010354. 



176 



ELEMENTARY LESSONS ON [chap, iil 



" equivalent " 1 of copper is 31*5; multiplying this by 
•000010352 we get as the electro-chemical equivalent of 
copper the value •0003261 (gramme). 

212. Table of Electro-chemical Equivalents, etc. 



[ 








Electro-chemical 




Atomic 


Val^ 


Chemical 


Equivalent 




Weight. 


ency. 


Eauivalent. 


(grammes 
per c&ulovib). 


Electropositive — • 










Hydrogen . . , , 


I' 


I 


I 


•000010352 


Potassium .... 


39-1 


I 


39-1 


•0004047 


Sodium ..... 


23- 


I 


23- 


•0002381 


Gold 


196^6 


3 


65-5 


•0006780 


Silver 


108- 


I 


io8- 


•001 1 180 


Copper (Cupric) . . 


63- 


2 


31-5 


•0003261 


'„ (Cuprose) . 


63- 


I 


63- 


'OO06522 


Mercury (Mercuric) . 


200* 


2 


lOO' 


•0010351 


,, (Mercurose) 


200' 


I 


2uO' 


•0020702 


Tin (Stannic) . . . 


ii8- 


4 


29-5 


•0003054 


,, (Stannose) 


ii8- 


2 


59- 


'OO0610S 


Iron (Ferric) . . . 


56- 


3 


18 -6 


0*0001932 


„ (Ferrose) . . 


56- 


2 


28- 


•0002898 


Nickel 


59- 


,2 


29-5 


•0003054 


Zinc . . . . . 


65. 


2 


32-5 


•0003364 


Lead ..... 


207* 


2 


103-5 


•00 1 068 i 


Electronegative — ;, 










Oxygen . . *, , 


i6- 


2 


8- 


•0000828 


Chlorine .... 


3S-S 


I 


35-5 


•0003675 


Iodine ..... 


127- 


I 


127- 


•OOI3147 


Bromine .... 


8o- 


I 


8o- 


•0008282 


Nitrogen .... 


M- 


3^ 


4-3 


'OOOO445 



1 The chemical ''equivalent'' must not be confounded with the *^ aiomk 

vjei\^hi,** The atomic weight of copper is 63, that is to say, its atoms are 63 

times as heavy as atoms of hydrogen. But in chemical combinations one 

atom of copper replaces^ or is " worth," two atoms of hydrogen ; hence the 

weight of copper equivalent to i of hydrogen is V ^ 3i|. In all cases the 

1 . I <r . , „ . , . atomic weifjht. „ ,. 

chemical equivalent" is the quotient .,^i^.,;: .7^ — The above Tabb 

gives full statistical information. 



valency 



CHAP. III.] ELECTRICITY AND MAGNETISM. 177 

213. The following equation embodies the rule for 
finding the weight of any given ion disengaged from an 
electrolytic solution during a knov^m time by a current 
whose strength is known. Let C be the strength of the 
current (reckoned in a7np}res\ t the time (in seconds), 
z the electro-chemical equivalent, and w the weight (in 
grammes) of the element liberated ; then 

w = ^C/, 

or, in words, the weight (in grammes) of an elemeni 
deposited by electrolysis is found by multiplying its 
electro-chemical equivalent by the strength of the current 
(reckoned in ampires)^ and by the time (in seconds)^ 
duriftg which the current co7ttinues to flow. 

Example.— A current from five Darnell's cells was passed 
through two electrolytic cells, one containing a solution 
of silver, the other acidulated water, for ten minutes. 
A tangent galvanometer in the circuit showed the 
strength of the current to be 'S amperes. The weight 
of silver deposited will be 'OOiiiSo x '5 x 10 x 60 
= '3354 gramme. The weight of hydrogen evolved 
in the second cell will be '000010352 x -5 x 10 x 60 
= •0031056 gramme. 

214. Voltameters. — The second of the above laws, 
that the amount of an ion liberated in a given time is 
proportional to the strength of the current, is sometimes 
known as Faraday s Law^ from its discoverer. Faraday 
pointed out that it affords a chemical means of measur- 
ing the strength cf currents. He gave the name of 
voltameter to an electrolytic cell arranged for the 
purpose of measuring the strength of the cun-ent by 
the amount of chemical action it ejffects. 

215. Water -Voltameter. — The apparatus shown 
in Fig. 92 might be appropriately termed a Water- 
Voltameter, provided the tubes to collect the gases 
be graduated, so as to measure the quantities evolved* 



178 ELEMENTARY LESSONS ON [chap, m 

The weight of each measured cubic centimetre of hydro 
gen (at the standard temperature of o^ C, and pressure 
of 760 millims.) is known ♦to be -0000896 gramrries. 
Hence, if the number .of cubic centimetres liberated 
during a given time by a current of unknown strength 
be ascertained, the strength of the current can be calcu- 
lated by first reducing the volume to weight, and then 
dividing by the electro-chemical equivalent, and by the 
time. Each coulomb of electricity liberates in its flow 
•I 1 57 cubic centimetres of hydrogen, and '0579 c. c. 
of oxygen. If these gases are collected together in a 
mixed-gas voltameter there will be '1736 c. c. of the 
mixed gases evolved for every coulomb of electricity 
which passes. To decompose 9 grammes of water, 
liberating i gramme of H and 8 grammes of O, requires 
96,600 coulombs. 

216. Copper and Silver Voltameters. — As mentioned 
above, if sulphate of copper is electrolysed between two elec- 
trodes of copper, the anode is slowly dissolved, and the kathode 
receives an equal quantity of copper as a deposit on its surface.' 
One coulomb of electricity will cause '0003261 gramme to be 
deposited ; and to deposit one gramme weight requires a total 
quantity of 3066 coulombs to flow through the electrodes* A 
current of one «/?jf/<^r^ deposits in one hour 1*174 grammes of 
copper, or 4*025 grammes of silver. 

By weighing one of the electrodes before and after the passage of a current, 
the gain (or loss) v/ill be proportional to the quantllv of electricity that has 
passed. In 1879 Edison, the inventor,^ proposed to apply this method for 
measuring the quantity of electricity supplied to houses for electric lights in 
them ; a small copper Vcltameter being placed in a branch of ihe circuit 
which supplied the house, to serve as a meter. Various other kinds o^ 
Coulombmeters have been proposed, having clockwork counters, rolling 
integrating discs, and other mechanical devices to add up the total quantity 
of electricity conveyed by the current 

217. Comparison of Voltameters with Gal- 
vanometers. — It will be seen that both Galvanojnelers 
and Voltameters are intended to measure the strength o\ 
currents, one by magnetic, the other by chemical mearis.. 
Faraday demonstrated that the magnetic and the chemical 
actions of a current are proportional to one another 



CHAP. III.] ELECTRICITY AND MAGNETISM. 179 

The galvanometer shows, however, the strength of the 
current at any moment, and its variations in strength 
from one moment to another, by the position of the 
needle. In the Voltameter, a varying current may 
liberate the bubbles of gas or the atoms of copper rapidly 
at one moment, and slowly the next, but all the varying 
quantities will be simply added together in the total 
yield. In fact, the voltameter gives us the " time 
integral " of the current. It tells us what quantity of 
electricity has flowed through it during the experiment, 
rather than how strong the current was at any one 
moment. 

218. Chemical Test for Weak Ourrents. — A 
very feeble current suffices to produce a perceptible 
amount of change in certain chemical substances. If 
a few crystals of the white salt iodide of potassium are 
dissolved in water, and then a little starch paste is added, 
a very sensitive electrolyte is obtained, which turns to 
an indigo blue colour at the anode when a very weak 
current passes through it. The decomposition of the 
salt liberates iodine at the anode, which, acting on the 
starch, forms a coloured compound. White blotting- 
paper, dipped into the prepared liquid, and then laid on 
the kathode and touched by the anode, affords a con- 
venient way of examining the discoloration due to a 
current. A solution of Ferrocyanide of Potassium affords 
similarly on electrolysis the well-known tint of Prussian 
Blue. Bain proposed to utilise this in a Chemical 
Writing Telegraph, the short and long currents trans- 
mitted along the line from a battery being thus recorded 
in blue marks on a strip of prepared paper, drawn along 
by clockwork under the terminal of the positive wire. 
Faraday showed that chemical discoloration of paper 
moistened with starch and iodide of potassium was pro- 
duced by the passage of all different kinds of electricity*^ 
frictional, voltaic, thermo-electric, and magneto -elecUiG, 
— even by that evolved by the Torpedo and the 



fSo . ELEMENTARY LESSONS ON [chap. in. 

Gymnotus. In fact, he relied on this chemical test as 
one proof of the identity of the different kinds. 

219. Internal and External Actions. — In an 
earlier Lesson it was shown that the quantity of chemical 
action inside the cells of the battery was proportional to 
the strength of the current. Hence, Law (i.) of Art. 211, 
applies both to the portion of the circuit within the 
l^attery and to that without it. 

Suppose 3 Daniell's cells are being employed to decompose 
water in a voltameter. Then while i gramme 'weight (11,200 
cub, centims.) of hydrogen and 8 grammes (S,6oo c. c) of 
oxygen are set free in the voltameter, 3 1*5 grammes of cupper 
will be deposited in each cell of the battery, and (neglecting loss 
ky local action), 32 5 grammes of zinc will be dissolved m each 
cell 

220. It will therefore be evident that the electrolj^tic 
cell is the converse of the \oltaic cell. The chemical work 
done in the voltaic cell furnishes the energj' of the cunent 
which that cell sets up in the circuit. In the electrol3'tic 
cell chemical work is performed, the necessary energy 
being furnished by the current of electricity which is 
sent into the cell from an independent battel y or other 
source. 

A theory of electrolysis, and some examples of its 
application, are given in Chapter XXXYIII. on Electro- 
chemistry. 



Lesson XIX. — Physical and Physiological Effects of 
the Current. 

221. Molecular Actions. — :Metal conductors, when 
subjected to the prolonged action of currents, undergo 
slow molecular changes. Wires cf copper and brass 
gradually become brittle under its influence. During 
the passage of the current through metallic wires their 



CHAP, in.] ELECTRICITY AND MAGNETISM. 181 

cohesion is temporarily lessened, and there also appears 
to be a decrease in their coefficient of elasticity. It was 
thought by Edlund that a definite, elongation could be 
observed in strained wires when a current was passed 
through them ; but it has not yet been satisfactorily 
shown that this elongation is independent of the elonga- 
tion due to the heating of the wire owing to the resistance 
it opposes to the current. 

222. Electric Osmose. — Porret observed that if a 
strong current is led into certain liquids, as if to electro- 
lyse them, a porous partition being placed between the 
electrodes, the current mechanically carries part of the 
liquid through the porous diaphragm, so that the liquid 
is forced up to a higher level on one side than on the 
other. This phenomenon, known as electric osmose^ is 
most manifest when badly conducting liquids, such as 
alcohol and bisulphide of carbon, are used. The transfer 
through the diaphragm takes place in the direction of 
the current ; that is to say, the liquid is higher about 
the kathode than round the anode. 

223. Electric Distillation. — Closely connected 
with the preceding phenomenon is that of the electric 
distillation of liquids. It was noticed by Beccaria that 
an electrified liquid evaporated more rapidly than one 
not electrified. Gernez has recently shown that in a 
bent closed tube, containing two portions of liquid, one 
of which is made highly + and the other highly - , the 
liquid passes over from -f to - This apparent distilla- 
tion is not due to difference of temperature, nor does it 
depend on the extent of surface exposed, but is effected 
by a slow creeping of the liquid along the interior surface 
of the glass tubes. Bad conductors, such as turpentine, 
do not thus pass over. 

224. Diaphragm Currents. — Professor Quincke 
discovered that a current is set up in a liquid when it is 
forced by pressure through ^ porous diaphragm. This 
phenomenon may be regarded as the converse of electric 



i82 ELEMENTARY LESSONS ON [chap. III. 

osmose. The E.M.F. of the current varies with the 
pressure and with the nature of the diaphragm. When 
water was forced at a pressure of one atmosphere 
through sulphur, the difference of potential was over 9 
volts. With diaphragms of porcelain and bladder the 
differences were only -35 and -oi volts respectively. 

225. Electro-Capillary Phenomena. — If a hori- 
zontal glass tube, turned up at the ends, be filled with 
dilute acid, and a single drop of mercury be placed at 
about the middle of the tube, the passage of a current 
through the tube will cause the drop to move along 
towards the negative pole. It is believed that the 
liberation of very small quantities of gas by electrolysis at 
the surface where the mercury and acid meet alters the 
surface-tension very considerably, and thus a movement 
results from the capillary forces. Lippmann, Dewar. 
and others, have constructed upon this principle capillary 
electrometers^ in which the pressure of a column of liquid 
is made to balance the electro-capillary force exerted at 
the surface of contact of mercury and dilute acid, the 
electro-capillary force being nearly proportional to the 
electromotive-force when this does not exceed one volt. 
Fig. 93 shows the capillary electrometer of Dewar. 
A glass tube rests horizontally between two glass dishes 
in which holes have been bored to receive the ends of 



Fig. 93. 

the tube. It is filled with mercury, and a single drop 
of dilute acid is placed in the tube. Platinum wires to 
serve as electrodes dip into the mercury in the dishes. 
An E.M.F. of only gj^ volt suffices to produce a measure- 



CHAP. III.] ELECTRICITY AND MAGNETISM. 183 

able displacement of the drop. The direction of the 
displacement varies with that of the current. 

226. Physiological Actions. — Currents of elec- 
tricity passed through the limbs affect the nerves with 
certain painful sensations, and cause the muscles to 
undergo involuntary contractions. The sudden rush of 
even a small charge of electricity from a Leyden jar 
charged to a high potential, or from an induction coil 
(see Fig. 148), gives a sharp and painful shock to the 
system. The current from a few strong Grove's cells, 
conveyed through the body by grasping the terminals 
with moistened hands, gives a very different kind of 
sensation, not at all agreeable, of a prickling in the joints 
of the arms and shoulders, but not producing any 
spasmodic contractions, except it be in nervous or 
v/eakly persons, at the sudden making or breaking of 
the circuit. The difference between the two cases lies 
in the fact that the tissues of the body offer a very con- 
siderable resistance, and that the difference of potential 
in the former case may be many thousands of volts ; 
hence, though the actual quantity stored up in the 
Leyden jar is very small, its very high E.P^I.F. enables 
it at once to overcome the resistance. The baiitery, 
although it might, when working through a good con- 
ductor, afford in one second a thousand times as much 
electricity, cannot, when working through the high re- 
sistance of the body, transmit more than a small fraction, 
owing to its limited E.M.F. 

After the discovery of the shock of the Leyden jar by 
Cuna^us in 1745 many experiments were tried, Louis 
XV. of France caused an electric shock from a battery of 
Leyden jars to be administered to 700 Carthusian monks 
joined hand in hand, with prodigious effect. Franklin 
killed a turkey by a shock from a Leyden jar. 

227. In 1752 Sulzer remarked that *^ if you join two 
pieces of lead and silver, and then lay them upon the 
tongue, you will notice a certain fasi^ resembling that of 



I84 ELEMENTARY LESSONS ON [chap, in, 

green vitriol, while each piece "^ apart produces no such 
sensation.-' This galvanic tastej not then suspected 
to have any 'connection with electricity, may be ex- 
perienced by placinj^ a silver coin on the tongue and a 
steel pen under it, the edges of them being then brought 
into metallic contact. The same taste is noticed if the 
two wires from the poles of a voltaic cell are placed in 
contact with the tongue. 

228. Ritter discovered that a feeble current trans- 
mitted through the eyeball produces the sensation as of 
a bright ^as/i of light ,hy its sudden stimulation of the 
optic nerve. A stronger current transmitted by means 
of moistened conductors attached to the battery terminals 
gave a sensation of blue and green colours in flowing 
between the forehead and the hand. Helmholtz, re- 
peating this experiment, observed only a wild rush of 
colour. Dr. Hunter saw flashes of light when a piece 
of metal placed under the tongue was touched against 
another which touched the moist tissues of the eye. 
Vblta and Ritter heard musical sounds when a current 
was passed through the ears : and Humboldt found a 
sensation to be produced in the organs of smell when a 
current was passed from the nostril to the soft palate. 
Each of the specialised senses can be stimulated into 
activity by the current. Man possesses no specialised 
sense for the perception of electrical forces, as he does 
for .light and for sound ; but there is no reason for denying 
the possibility that some of the lower creatures may be 
endowed with a special electrical sense. 

The following experiment shows the effect of feeble 
currents on cold-blooded creatures. * If a copper (or silver) 
coin be laid on a piece of sheet zinc, and a common 
garden snail be set to ^ crawl ' over the zinc, directly 
it comes into contact with the copper it will suddenly 
jpull in its horns, and shrink in its body. If it is set to 
crawl over two copper wires, which are then placed in 
contact with a feeble voltaic cell, it immediately an- 



CHAP. III.] ELECTRICITY AND MAGNETISM. 



185 



nounces the establishment of a current by a similar 
contraction. 1 

229. Muscular Contractions. — In 1678 Swam- 
merdam showed to the Grand Duke of Tuscany that when 
a portion of muscle of a frog's leg hanging by a thread of 
nerve bound with silver wire was held over a copper 
support, so that both nerve and wire touched the copper, 
the muscle immediately contracted. More than a cen- 




Fig. 94. 

tury later Galvani's attention was drawn to the subject 
by his observation of spasmodic contractions in the legs 
of freshly-killed frogs under the influence of the " return- 
shock " experienced every time a neighbouring electric 
machine was discharged. Unaware of Swammerdam's 
experiment, he discovered in 1786 the fact (alluded to in 

1 Tt will scarcely be credited that a certain Jules Alix once seriously pro- 
posed a system of telegraphy based on this physiological phenomenon. 



£S6 ELEMENTARY LESSONS ON [chap, jif 

Art. 148 as leading ultimately to the aiscovery of tne 
Voltaic Pile) that when nerve and muscle touch two 
dissimilar metals in contact with one another a ct)n. 
traction of the muscle takes place. The limbs of the 
frog, prepared as directed by Galvani, are shown in Fig. 
94. After the animal has been killed the hind limbs 
are detached and skinned ; the crural nerves and their 
attachments to the lumbar vertebras remaining. For 
some hours after death the limbs retain their contractile 
power. The frog's limbs thus prepared form an ex- 
cessively delicate galvanosccpe : with them, for example, 
the excessively delicate induction-currents of the tele- 
phone (Lesson XL.) can be shown, though the most 
sensitive galvanometers barely detect them. Galvani 
and Aldini proved that other creatures undergo like 
effects. With a pile of 100 pairs Aldini experimented 
on newly killed sheep, oxen, and rabbits, and found them 
to suffer spasmodic muscular contractions. Humboldt 
proved the same on fishes ; and Zanotti, by sending a 
current through a nev/ly killed grasshopper, caused it to 
emit its familiar chirp. Aldini, and later Dr. Ure of 
Glasgow^ experimented on the bodies of executed crimi- 
nals, with a success terrible to behold. The facial 
muscles underwent horrible contortions, and the chest 
heaved with the contraction of the diaphragm. This 
has suggested the employment of electric currents as an 
adjunct in reviving persons who have been drowned, the 
contraction of the muscles of the chest serving to start 
respiration into activity. The small muscles attached 
to the roots of the hairs of the head appear to be 
be markedly s'ensitive to electrical conditions from the 
readiness with v/hich electrification causes the hair to 
stand on end. 

230. Conditions of Muscular Contraction. — To 
produce muscular contraction the current must traverse 
a portion of the nei^ve longitudinally. In a freshly pre- 
pared frog the current causes a contraction only momen- 



CHAP. III.) ELECTRICITY AND MAGNETISM. 187 

tanly when the circuit is made or broken. A rapidly 
interrupted current will induce a second contraction 
before the first has had time to pass off, and the muscle 
may exhibit thus a continuous contraction resembling 
tetanus^ The prepared frog after a short time becomes 
less sensitive, and a " direct " current (that is to say, one" 
passing along the nerve in the direction from the brain 
to the muscle) only produces an effect when circuit is 
made, while an *' inverse'^ current only produces an 
effect when the circuit is broken. Matteucci, who 
observed this, also discovered by experiments on living 
animals that there is a distinction between the con- 
ductivity of sensory and motor nerves, — a ** direct " 
current affecting the motor nerves on making the 
circuit, and the sensory nerves on breaking it ; while 
an *' inverse '' current produced inverse results. Little 
is, however, yet known of the conditions of con- 
ductivity of the matter of the nerves ; they conduct 
better than muscular tissue, cartilage, or bone ; but of 
all substances in the body the blood conducts best. 
Powerful currents doubtless electrolyse the blood to 
some extent, coagulating it and the albumin it contains. 
The power of contractmg under the influence of the 
current appears to be a distinguishing property of 
protoplasm wherever it occurs. The amoeba, the 
most structureless of organisms, suffers contractions, 
Ritter discovered that the sensitive plant shuts up when 
electrified, and Burdon Sanderson has shown that this 
property extends to other vegetables, being exhibited by 
the carnivorous plants the Dioncea or Venus' Fly Trap. 

231. Animal Electricity. — Although, in his later 
writings at least, Galvani admitted that the electricity 
thus operating arose from the metals employed, he 
insisted on the existence of an animal electricity xts\ditni 
in the muscular and nervous structures. He showed 
that contractions could be produced without using any 
metals at all by merely touching a nerve at two different 



i88 ELEMENTARY LESSONS ON [chap. hi. 

points along its length with a morsel of muscle cut irom 
a living frog ; and that a conductor of one metal when 
joining a nerve to a muscle also sufficed to cause con- 
traction in the latter. Galvani and Aldini regarded 
these facts as a disproof of Volta's contact -theory. 
Volta regarded them as proving that the contact 
between nerve and muscle itself produced (as in the 
case of two dissimilar metals) opposite electrical con- 
ditions. Nobili, later, showed that when the nerve and 
the muscle of the frog were respectively connected by a 
water -contact with the terminals of a delicate galvan- 
ometer, a current is produced which lasts several hours : 
he even arranged a number of frogs' legs in series, 
like the cells of a battery, and thus increased the current. 
Matteucci showed that through the muscle alone there is 
an electromotive-force. Du Bois Reymond has shown 
that if the end of a muscle be cut across, the ends of the 
muscular fibres of the transverse section are negative, 
and the sides of the muscular fibres are positive, and 
that this difference of potential will produce a current 
even while the muscle is at rest. To demonstrate this 
he employed a fine astatic galvanometer with 20,000 
turns of wire in its coils ; and to obviate errors arising 
from the contact of the ends of the v/ires with the tissues 
unpolarisable electrodes were used, made by plunging 
terminal zinc points into a saturated solution of sulphate 
of zinc, contained in a fine glass tube, the end of which 
was stopped with a porous plug of moistened china clay. 
The contraction of muscles also produces currents. 
These Du Bois Reymond obtained from his own muscles 
by dipping the tips of his fore -fingers into two cups 
of salt water communicating with the galvanometer 
terminals. A sudden contraction of the muscles ci 
either arm produced a current from the contracted 
toward the uncontracted muscles. Dewar has shown 
that when light falls upon the retina of the eye an 
ekctric current is set up in the optic nerve. 



CHAP. III.] ELECTRICITY. AND MAGNETISM. 189 

232. Medical Applicationa — Electric currents 
have been succ^sfully employed as an adjunct in 
restoring persons rescued from drowning; the contrac- 
tion of the diaphragm and chest muscles serving to start 
respiration. Since the discovery of the Leyden jar 
many attempts have been made to establish an electrical 
medical treatment. Discontinuous currents, particularly 
those furnished by small induction-coils and magneto- 
electric machines, are employed by practitioners to 
stimulate the nerves in paralysis and other affections. 
Electric currents should not be used at all except with 
great care, and under the direction of regularly trained 
surgeons.^ 

1 It is not out of place to enter an earnest caution on this head against the 
numerous quactc doctors who deceive the unwary with magnetic and 
galvanic "appliances." In many cases the«;e much-advertised shams have 
done incalculable harm : in the very few cases where some faficied good has 
accrued the curative agent is probably not ma^^ietismi but flannel 1 



190 ELEMENTARY LESSONS ON [chap. tv. 



CHAPTER IV. 

Electrostatics. 

Lesson XX. — Theory of Poleniial. 

233. Bj' the Lessons in Chapter L the student will 
have obtained some elementary notions upon the exist- 
ence and measurement of definite quantities of electricity. 
In the present Lesson, which is both one of the hardest 
and^ one of the most important to the beginner, and 
which he must therefore study the more carefully, the 
laws which concern the magnitude of electrical quantities 
and their measurement are more fully explained. . In no 
branch of knowledge is it more true than in electricity, 
that *• science is measurement." That part of the science 
of electricity which deals with the measurement of 
charges of electricity is called Electrostatics. We 
shall begin by discussing first the simple laws of electric 
force, which were brought to light in Chapter. I. by 
simple experimental means. 

234. First Law of Electrostatics. — Electric 
charges of similar sign repel one another^ hut electric 
charges of opposite signs attract one another. The funda- 
mental facts expressed in this Law were fully explained 
in Lesson I. Though familiar to ' the student, and 
apparently simple, these facts require for their complete 
explanation the aid of advanced mathematical analysis. 
They will here be treated as sample facts of observation. 



CHAP, iv.l ELECTRICITY AND MAGNETISM. 191 

235. Second Law of Electrostatics. — The force 
exerted between two charges of electricity (supposing them 
to be collected at points or on two small spheres), is 
directly proportional to their product^ and inversely 
proportional to the square of the distance between them. 
This law, discovered by Coulomb, and called Coulomb's 
Law, was briefly alluded to (on page 16) in the account 
of experiments made with, the torsion -balance ; and 
examples were there given in illustration of both parts of 
the law. We saw, too, that a similar law held good for 
the forces exerted between two magnet poles. Coulomb 
applied also the method of oscillations to verify the 
indications of the torsion-balance and found the results 
entirely confirmed. We may express the two clauses of 
Coulomb's law, in the following symbolic manner. Let 
/stand for the force, q for the quantity of electricity in 
one of the two charges, and q' for that of the other 
charge, and let d stand for the distance between them. 
Then, 

(i.) /is proportional to ^ x q\ 

and (2.) /is proportional to™ 

These two expressions may be combined into one ; 
and it is most convenient so to choose our units or 
standards of measurement that we may write our symbols 
as an equation : — 

236. Unit of Electric Quantity. — If we are, how- 
ever, to write this as an equality, it is clear that we 
must choose our unit of electricity in accordance with 
the units already fixed for measuring force and distance. 
All electricians are now virtually agreed in adopting a 
system which is based upon three fundamental units: 
viz., the Oentiraetre for a unit of length; the Gramnae 
for a unit of ma^s , the Second for a unit of time, AU 



192 ELEMENTARY LESSONS ON [chap. iv. 

other units can be derived from these, as is explained 
in the Note at the end of this Lesson. Now, amongst 
the derived units of this system is the unit of force^ 
nam ad the Dyne, which is that force which, acting for 
one second on a mass of one gramme, imparts to it 
a velocity of one centimetre per second. Taking the 
dyne then as the unit of force, and the centimetre as 
the unit of length (or distance), we must find a unit of 
electric quantity to agree with these in our equation. 
It is quite clear that if ^, /, and d were each made equal 
to I (that is, if we took two charges of value i each, 
and placed them one centimetre apart), the value of 

^2 would be YlTi ^^^^^ ^^ equal to i. Hence we 
idopt, as our Definition of a Unit of Electricity^ the 
following, which we briefly gave at the end of Lesson II. 
One Unit of Electricity is that quantity which , when placed 
at a distance of one centimetre {in air) from a similar and 
equal quantity ^ repels it with a force of one dyne. 

An example will aid the student to understand the 
application of Coulomb's law. 

Example.— Two small spheres, charged respectively with 
6 units and 8 units of + electricity, are placed 4 
centimetres apart ; find what force they exert on one 

another. By the formula, /= ^^-^^ we find/ = 

— g- = ~ = 3 dynes. Examples for the student 
are given in the Questions at the end of the Book. 

The force in the above example would clearly be a force 
of repulsion. Had one of these charges been negative, 
the product q y> q' would have had a - value, and the 
answer would have come out as minus 3 dynes. The 
presence of the negative sign, therefore, prefixed to a 
force, will indicate that it is a force of attraction^ whilst 
the + sign would signify a force of repulsion. 

237. Potential. — We must next define the term 
potential^ as applied to electric forces ; but to make 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 193 

the meaning plain a little preliminary explanation is 
necessary. Suppose we had a charge of + electricity 
on a small insulated sphere A (See Fig. 95), placed by 
itself and far removed from all other electrical charges 
and electrical conductors. If we were to bring another 
body B near it, charged also with + electricity, A would 
repel B. But the repelling force would depend on the 
quantity of the new charge, and on the distance at which 
it was placed. Suppose the new charge thus brought 

A P Q B^ B' 

Q«..„™ „ — .-o-- — ^««-.-.»..e-"™" — -e--— 

Fig. 95. 

near to be one unit of + electricity ; when B was a long 
way off it would be repelled with a very slight force, and 
very little work need be expended in bringing it up 
nearer against the repelling forces exerted by A ; but as 
B was brought nearer and nearer to A, the repelling 
force would grow greater and greater, and more and 
more work would have to be done against these oppos- 
ing forces in bringing up B. Suppose that we had 
begun at an infinite distance away, and that we pushed 
up our little test charge B fronci B' to B" and then to Q, 
and so finally moved it up to the point P, against the 
opposing forces exerted by A, we should have had to 
spend a certain amount of work; that work represents 
the potential^ at the point P due to A. For the follow- 
ing is the definition of electrostatic potential: — The 
potential at any. point is the work that must be spent 

1 In its widest meaning the term *^ potential''^ must be understood as 
** power to do work." For if we have to do a certain quantity of work 
against the repelling force of a charge in bringing up a unit of electricity 
from an infinite distance, just so much work has the charge power to do, for 
it will spend an exactly equal amount of work in pushing the unit of electri- 
city back to an infinite distance. If we lift a pound five feet high against 
the force of gravity, the weight of the pound can in turn do five foot-pounds 
of work in falling back to the ground. See the Lesson on Energy in Pro- 
fessor Balfour Stewart's Lessons in Elementary Physics. 

O 



f94 ELEMENTARY LESSONS ON [chap. iv. 

Upon a unit of positive electricity i7i bringi?vg it up to 
that point from an infinite distance. Had the charge on 
A been a - charge, the force would have been one of 
attraction, in which case we should have theoretically to 
measure the potential at P, either by the opposite 
process of placing there a + unit, and then removing it 
to an infinite distance against the attractive forces, or 
else by measuring the amount of work which would be 
done 6y 2i + unit in being attracted up to P from an 
infinite distance. 

It can be shown that where there are more electrified 
bodies than one to be considered, the potential due to 
them at any point is the sum of the potentials (at that 
point) of each one taken separately. 

238. It can also be shown that the potential at a 
point P, near an electrified particle A, is equal to the 
quantity of electricity at A divided by the distance 
between A and P. Or, if the quantity be called ^, and 

the distance r, the potential is ^."^ If there are a 

number of electrified particles at different distances 

from P, the separate values of the potential -? due to 

each electrified particle separately can be found, and 
therefore t/ie potential at P can be found by dividijtg the 
quantity of each charge by its distance from the point P^ 
and then adding tip together the separate amounts so 
obtai?ted. The symbol V is generally used to represent 
potential. The potential at point P we v/ill call Vp, then 



or Vp = 2l 



V„ = 1 + 1. ^ ^ 4- etc 



This expression 2 ^ represents the work done on oi 

• The complete proof would require an elementary application of the 
integral cafculus, but an easy geometrical demonstration, sufficie:ni for 
present purposes, is given below. 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 195 

by a unit of -f electricity when moved up to the given 
point P from an infinite distance, according as the 
potential at P is posjtive or negative. 

Proof. — First deiernHne the difference of potential between 
point P and point Q due to a charge of electricity f on a small 
sphere at A. 



®- 



111, 1 h-f- 

^ ^i ^Q ^s rn-ir' 



Fig. 96. 

Call distance AP = r, and AQ = r". Then PQ = 
/ — n The difference of potential between Q and P is the 
work done in moving a + unit from Q to P against the force ; 
and since 

work = (average) force x distance through which it 
is overcome 

Vp- Vq =/(.^->;. 

The force at P exerted by f on a + unit = \f 
and the force at Q exerted by f on a + unit = ^. 

Suppose now that the distance PQ be divided info znj 
number («) of equal parts rrj, rir^, r^r^, rn-ir' . 



The force at r = ^. 



= ^ . . . etc. 



'1 

Now since r, may be made as close to ^ as we choose, if we 
only take f/ a large enough number, we shall commit no serious 
error in supposing that r x r^ is a fair mean between r^ and 
rj- ; hence we may assume the average force over the short 

length feom r to r^ lo be -^. 



195 ELEMENTARY LESSONS ON [chap nr. 

Hence the work done in passing from ri to r will be 

= ?(-r-i) 

On a similar assumption, the work done in passing from r^ 
to rj, will be 

=^ ^ ( "~ "" ~' ) » ^^^ ^^^^ ^^^^ fro^ ^3 ^^ ^2 ^U be 

r= ^ ( — - — h etc., giving us n equations, of which* 

the last will be the work done in passing from r to r„., 

Adding up all these portions of the work, the intermediate 
values of r cancel out, and we get for the work done in pass- 
ing from Q to P 

Next suppose Q to be an infinite distance from A. Here 
r' = infinity, and -^ = o. In that case the equation 

becomes ^ 

V = i- 
p r 

If instead of one quantity of electricity ^, there were a 
number of electrified particles having charges ^, /', ^^ . . , . 

etc., at distances of r\ r\ r" etc., respectively from 

P. then 

-^—JT -K - - - . . . etc 

which was to be proved. 

239, Zero PotentiaL — At a place infinitely distant 
from all electrified bodies there would be no electric 
forces and the potential would be zero. For purposes 
of convenience it is, however, usual to consider the 
potential of the earth for the time being as an arbitrary 



V ^ 


-4- 


Vp = 2 


r ' 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 197 

zero, just as it is convenient to consider " sea-level " as 
a zero from which to measure heights or depths. 

240. Difference of Potentials. — Since potential 
represents the work that must be done on a + unit in 
bringing it up from an infinite distance, the difference 
of potential between two points is the work to be done on 
or by a -^r unit of electricity in carrying it from one point 
to the other. Thus if Vp represents the potential at P, 
and Vq the potential at another point Q, the difference 
of potentials Vp - Vq denotes the work done in moving 
up the -f unit from Q to P. It is to be noted that since 
this value depends only on the values of the potential 
at P and at Q, and not on the values of the potential at 
intermediate points, the work done will be the same, 
whatever the path along which the particle moves from 
Q to P. In the same way it is true that the expenditure 
of energy in lifting a pound against the earth's attraction 
from one point, to another on a higher level, will be the 
same whatever the path along which the pound is lifted. 

241. Eleotrio Force. — The definition of " work " is 
the product of the force overcome into the distance 
through which the force is overcome, or work = force 

X distance through which it is overcome. 

Hence, if the difference of potential between two 
points is the work done in moving up our -f unit from 
one point to the other, it follows that the average electric 
force between those points will be found by dividing 
the work so done by the distance between the points : 

or ^ " ^ =/ (the average electric force along the line 

PQ). The (average) electric force is therefore the rate 
of change of potential per unit of length. If P and Q 
are near together the force will be practically uniform 
between P and Q. 

242. Equipotential Surfaces.— A charge of elec- 
tricity collected on a small sphere acts on external 
bodies as if the charge were all collected into one point 



198 ELEMENTARY LESSONS ON [chaf. iv. 

at its centre,^ We have seen that the force exerted by 
such a charge falls off at a distance fiom the ball, the 
force becoming less and less as the square of the 
distance increases. But the force is the same in 
amount at all points equally distant from the small charged 
sphere. And the potential is the same at all points 
that are equally distant from the charged sphere. ^ If, in 
Fig. 96, the point A represents the sphere charged with 
q units of electricity, then the potential at P, which we 

will call Vp, will be equal to ^ where r is the distance 

from A to P. But if we take any other point at the 

same distance from A its potential will also be ^^ Now 

all the points that are the same distance from A as 
P is, will be found to lie upon the surface of a sphere 
whose centre is at A, and which is represented by the 
circle drawn through P, in Fig. 97. All round this circle 
the potential will have equal values ; hence this circle 
represents an equipotential surface. The work to 
be done in bringing up a + unit from an infinite distance 
will be the same, no matter what point of this equi* 
potential surface it is brought to,, and to move it about 
from oiie point to another in the equipotential surface 
requires no further overcoming of the electrical forces, 
and involves therefore no* further expenditure of work. 
At another distance, say at the point Q, the potential 
will have another value, and through this . point Q 
another equipotential surface may be drawn. Suppose 
we chose Q so far from P that to push up a unit of + 
electricity agaifist the repelling force of A required the 
expenditure of. just one erg of work (for the definition 

1 Th^ student must be warned that this ceases to be true if other charges 
are brought very near to the sphere, for then the electricity will no longer 
be distributed uniformly over its surface. It is for this reason that' we have 
said, in describing -the measurement of electrical forces with the torsion 
balance, that ** the balls must be very small in proportion to the distances 
between them«.'* 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 



199 



of one erg see the Note on Units at the end of this 
lesson) ; there will be then unit difference of potential 



A 

o 



^J? 



Fig. 97. 

between the surface drawn through Q and that drawn 
through P, and it will require one erg of work to carry 
a + unit from any point on the one surface to any point 
on the other. In like manner we might construct a 
whole systein of equipotential surfaces about the point A, 
choosing them at such distances that there should be 
unit difference of potential between each one and the 
next. The widths between them would get wider and 
wider, for, since the force falls off as you go further from 
A, you must, in doing one erg of work. Bring up the 
+ unit through a longer distance against the weaker 
opposing force. 

The form of the equipotential surfaces about two small 
electrified bodies placed near to one another would not 
be* spherical ; and around a number of electrified bodies 
placed near to one another the equipotential surfaces 
would be highly irregular in form. 

243. Lines of Force. — The electric force, whether 
of attraction or repulsion, always acts across the equi- 
potential surfaces in a direction normal to the surface. 
The lines which m.ark the direction of the resultant 
electric forces are sometimes called Lines of Electric 



200 ELEMENTARY LESSONS ON [chap. iv. 

Induction. In the case of the single electrified sphere 
the lines of force would be straight lines, radii of the sys- 
tem of equipotential spheres. In general, however, lines 
of force are curved ; in this case the resultant force at 
any point would be in the direction of th^- tangent to the 
curve at that point. Two lines of force cannot cut one 
another, for it is impossible ; the resultant force at a point 
cannot act in two directions at once. The positive 
direction along a line of force is that direction in which 
a small body charged with + electricity would be im- 
pelled by the electric force, if free to move. A space 
bounded by a number of lines of force is sometimes 
spoken of as a tube of force. All the space, for example, 
round a small insulated electrified sphere may be re- 
garded as mapped out into a number of conical tubes, 
each having their apex at the centre of the sphere. The 
total electric forc^ exerted across any section of a tube 
of force is constant wherever the section be taken. 

244. Potential within a Closed Conductor. — 
The experiments related in Arts. 29 to 32 prove most 
convincingly that there is no electric force inside a closed 
conductor. Now we have shown above that electric 
force is the rate of change of potential per unit of length. 
If there is no electric force there is no change of 
potential. The potential within a closed conductor (for 
example a hollow sphere) is therefore the same all over 
the interior ; the same as the potential of the surface. 
The surface of a closed conductor is therefore necessarily 
an equipotential surface. If it were not at one potential 
there would be a flow of electricity from the higher 
potential to the lower, which would instantaneously 
establish equilibrium and reduce the whole to one 
potential. The power of an electric system to do 
work does not depend upon the accidental surface- 
density at any one point. We know, for instance, 
that when an electrified body is placed near an insulated 
conductor the nearer and farther portions of that con- 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 201 

ductor exhibit induced charges of opposite kinds. The 
explanation of the paradox is that in the space round the 
charged body the potential is not uniform. Suppose the 
body to have a + charge, the potential near it is higher 
than in the space farther away. The end of the insulated 
conductor nearest to the charge is in a region of hi^ 
potential, while its farther end is in a region of lower 
potential. It will, as a whole, take a mean potential, 
which will, relatively to the potential of the surrounding 
medium, appear negative at the near end, positive at the 
far end. 

245. Law of Inverse Squares. — An important 
coftsequence follows from the absence of electric force 
inside a closed conductor ; this fact enables us to de- 
monstrate the necessary truth of the "law of inverse 
squares " which was first experimentally, though roughly, 
proved by Coulomb with the torsion balance. Suppose 
a' point P anywhere inside a hollow sphere charged with 
electricity (Fig. 98). The charge is uniform all over, 
and the quantity of electricity 
on any small portion of its 
surface will be proportional 
to the area of that portion. 
Consider a small portion of 
the surface AB. The charge 
on AB would repel a + unit 
placed at P with a certain 
force. Now draw the lines 
AD and BC through P, and 
regard these as mapping out 
a small conical surface of ^^^- 9^- 

two sheets, having its apex at P ; the small area CD 
will represent the end of the opposed cone, and the 
electricity on CD will also act on the + unit placed at P, 
and repel it. Now these surfaces AB and CD, and the 
charges on them, will be directly proportional to the 
squares of their respective distances from P. If, then 




202 ELEMENTARY LESSONS ON [chap, iv 



the forces which they exercise on P exactly neutralise 
one another (as experiment shows they do), it is clear 
that the electric force must fall off inversely as the 
squares of the distances; for the whole surface of the 
sphere can be mapped out similarly by imaginary cones 
drawn through P. The reasoning can be extended also 
to hollow Conductors of any form. 

246. Capacity. — In Lesson IV. tne student was 
given some elementary notions on the subject of the 
Capacity of conductors. We are now ready to give 
the precise definition. The Electrostatic Capacity of 
a .conductor is measured by the quantity of electricity 
which must be imparted to it in order to raise its potential 
from zero to unity, A small conductor, such as an 
insulated sphere of the size of a pea, >vill not want so 
much as one unit of electricity to raise its potential 
from o to I ; it is therefore of small capacity — while 
a large sphere will require a large quantity to raise its 
potential to the same degree, and would therefore be 
said to be of large capacity. If C stand for capacity, 
and Q for a quantity of electricity, 

C = ^ and C V = Q, 

This is equivalent to saying in words that the quantity 
of electricity necessary to charge a given conductor to 
a given potential,' is numerically equal to the product of 
the capacity into the potential through which it is raised. 

247. Unit of Capacity. — A conductor that required 
only one unit of electricity to raise its potential from o 
to I, would be^said to possess unit capacity. A sphere 
one centimetre in radius possesses unit capacity; for 
if it be charged with a quantity of one unit, this charge 
will act as if it were collected at its centre. At the 
surface, which is one centimetre away from the centre^ 

the potential, which is measured as •^, will be i. Hence, 

as I unit of quantity raises it to unit i of potential, the 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 203 

sphere possesses unit caj)acity. The capaciiies of spheres 
are proportional to- their radii. Thus, a sphere of one 
metre radius has a capacity of lop. The earth has a 
capacity of about 630 millions (m electrostatic units). 
It is "almost impossible to^ calculate the capacities of 
conductors of other shapes. It must be noted that the 
capacity of a sphere, as' given above, means its capacity 
when far removed from other conductors or charges oj 
electricity. The capacity of a conductor is increased by 
bringing near it a charge of an opposite kind ; for the 
potential at the surface of the conductor is the sum ol 
the potential due to its own charge, and of the potential 
of opposite sign due to the neighbouring charge. Hence, 
to, bring up the resultant potential to unity, a larger 
quantity of electricity must be given to it; or, in other 
words, Its capacity is greater. This is the true way of 
regarding the action of Leyden jars and other accumu- 
lators, and must be remembered by the student when he 
advances to the consideration of the theory of accumu- 
lators, in Lesspn XXII. 

248. Surface-density.^ — Coulomb applied this term 
to denote the amount of electricity per unit of area at any 
point of a surface. It was mentioned in Lesson IV. that 
a charge of electricity was never distributed uniformly 
oyer a conductor, except in the case of an insulated 
sphere. Where the distrib^ution is unequal, the density 
at any point of the surface may be expressed by con- 
sidering the quantity of elettricity which exists upon a 
small unit of area at that point. If Q be the quantity 
of electricity on the small surface, and S be the area of 

^ The word Tension is soinetimes used for that which is here precisqjy 
defined as Coulomb defined it. The term tension is, however, unfortunate ; 
and it is so often rnisapplied in text-books to mean not only surface-density 
but also potential, and even electric force (2.^., the mechanical force exerted 
upon a material body by electricity), that we avoid its use altogether. The 
term v/ould be invaluable if v/e might adppt it to denote only the mechanical 
stress across a dielectric, due to accumulated charges ; but so long as the 
above confusion lasts, it is better to drop the term entirely, and the student 
will have one thing fewer to learn -and to unlearn. 



204 ELEMENTARY LESSONS ON [chap. iv. 

that small surface, then the surface density (denoted by 
the Greek letter p) will be given by the equation, 

"=% 

In dry air, the Hmit to the possible electrification is 
reached v/hen the density reaches the value of about 20 
units of electricity per square centimetre. If charged to 
a higher degree than this, the electricity escapes in 
'* sparks " and " brushes '* into the ain In the case of 
um/orm distribution over a surface (as with the sphere, 
and as approximately obtamed on a flat disc by a parti- 
cular device known as a guard-ring), the density is found 
by dividing the whole quantity of the charge by the 
whole surface. 

249 Surface-Density on a Sphere. — The surface 
of a sphere whose radius is r, is 477^^. Hence, if a 
charge Q be imparted to a sphere of radius r, the surface- 

density all over will be p = — ^-; or, if we know the 

surface - density, the quantity of the charge will be 
Q - 4 wr^p. 

The surface-density on iwo spheres joined by a thin 
wire is an important case. If the spheres are unequal, 
they will share the charge in proportion to their capacities 
(see Art. 37), that is, in proportion to their radii. If the 
spheres are of radii 2 and i, the ratio of their charges 
will also be as 2 to 1. But their respective densities will 
be found by dividing the quantities of electricity on each 
by their respective surfaces. But the surfaces are pro- 
portional to the squares of the radii, /.<?., as 4 : i ; hence, 
the densities will be as i : 2, or inversely as the radii. 
Now, if one of these spheres be very small — no bigger 
than a point — the density on it will be relatively 
immensely great, so great that the air particles in con- 
tact with it will rapidly carry off the charge by convection. 
This explains the action of points in discharging con- 
ductors, noticed in Chapter I. Arts. 35 c^ 42 and 43. 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 205 

250. Electric Images. — It can be shown mathe- 
matically that if + ^ units of electricity are placed at a 
point near a non-electrified conducting sphere of radius 
r, at a distance d from its centre, the negative induced 

charge will be equal to — ^j', and wall be distributed over 

the nearest part of the surface of the sphere with a 
surface-density inversely proportional to the cube of the 
distance from that point. Sir W. Thomson pointed out 
that, So far as all external points are concerned, the 
potential due to this peculiar distribution on the suiface 
would be exactly the same as if this negative charge were 

all collected at an internal point at a distance of r — ~- 
behind the surface. Such a point may be regarded as a 
virtual image of the external point, in the same way as in 
optics we regard certain points behind mirrors as the 
virtual images of the external points from which the rays 
proceed. Clerk JMaxwell has given the following defini- 
tion of ail Electric Image : — An electric image is an 
electrified pointy or system of points^ on one side of a surface^ 
which would produce on the other side of that surface the 
same electrical action which the actual electrification oj 
that surface really does produce. A charge of -f- elec- 
tricity placed one inch from a flat metallic plate induces 
on it a negative charge distributed over the neighbouring 
region of the plate (with a density varying inversely as 
the cube of the distance from the point) ; but the 
electrical action of this distribution would be precibely 
represented by its " image," namely, by an equal quantity 
of negative electricity placed at a point one inch behind 
the plate. Many beautiful mathematical applications of 
this method have been made, enabling the distribution 
to be calculated in difficult cases, as, for example, the 
distribution of the charge on the inner surface of a hollow 
bowl. 

25L Electric Force exerted by a Charged 



2o6 ELEMENTARY LESSONS ON [chap. iv. 

Sphere at a point near to it. — It was shown 
above that the quantity of electricity Q upon a sphere 
charged until its surface-density was p, was 
Q = 4 irr^p. 
The problem is to find the force exercised by this 
charge upon a + unit of electricity, placed at a point 
infinitely near the surface of the sphere. The charge on 
the sphere acts as if at its centre. The distance between 
the two quantities is therefore r. By Coulomb's law the 

torce/ - -^ = — ^— = 4 7r/). 

This important result may be stated in words as 
follows : — The force (in dynes) exerted by -a charged 
sphere upon a unit of electricity placed i^tfinitely near to 
its surface^ is numerically equal to 47r times the surface- 
density of the charge. 

252. Electric Force exerted by a charged 
plate of indefinite extent on a point near it.— 
Suppose a plate of indefinite extent to be charged so that 
it has a surface-density p. This surface-density will be 
uniform, for the edges of the plate are supposed to be 
so far oflf as to exercise no influence. It can be shown 
that the force exerted by such a plate upon a -i- U7iit any- 
where near it, will be expressed (in dynes) numerically 
as 277/). This will be of opposite signs on opposite sides 
of tke plate, being + 2'n'p on one side, and - iirp on the 
other side, since in one case the force tends to move the 
unit from right to left, in the other from left to right 
It is to be observed, therefore, that the force changes its 
value by the amount of 47rp as the point passes through 
the surface. The same was true of the charged sphere, 
where the force outside was 47rp, and inside was zero. 
The same is true of all charged surfaces. These two 
propositions are of the utmost importance in the theory 
of Electrostatics. 

253. The elementary geometrical proof of the latter theorcHi 
is as follows : — 



CHAP, iv.] ELECTRICITY AND IMAGNETISM. 



207 



Required the Electric Fo7'ce at point at a^ty distance from a 
plane of infinite extent cnarged to siirface-de^isity p. 

Let P be the point, 

and PX or ^ the normal 

to the plane. Take any 

small cone having its 

apex at P. Let the 

solid-angle of this cone 

be (s>*, let its length be 

r; and the angle its 

axis makes with a. The 

cone meets the_ surface 

of the plane obliquely, 

and if an orthogonal 

section be made where 

it meets the plane, the 

angle between these sections will be = ^. 

T^T 1.-I 1 • 1 J /= •.• orthogonal area of section 
Now solid-angle w is by definition = ^^ _ 

Hence, area of oblique section = i^oj x 




Fig. 99. 



charge on oblique section = 



^(jjp 
cos d 



cos 6 



Hence if a + ufiit of electricity were placed at P, the force 

exerted on this by this small charge = — —^ x i -^ r^ 
' ^ cos ^ 



or 



_ cop 
cos 



Resolve this force into* two parts, one acting along the plane, 
the other along ^, normal to the plane. The normal component 
cop 



along ^ is cos ^ x 



cos 6 



= cop 



But the whole surface of the plane may be similarly mapped 
out into small surfaces, all forming small cones, with their summits 
at P. If we take an infinite number of such small cones meeting 
every part, and resolve their forces in a similar way, we shall 
find that the components along the plane will neutralise one, 
another all round, while the normal components, or the resolved 
forces along a, will be equal to the sum of all their solid-angles 
multiplied by the surface- density ; or 

Total resultant force along a = So?/). 



2oS ELEMENTARY LESSONS ON [chap, iv 



But the total solid -angle subtended by an infinite plane at a 
point is 2Tr^ for it subtends a whole hemisphere. 

.•. Total resultant force = 27rp, 



NOTE ON FUNDAMENTAL AND DERIVED UNITS. 

254. Fundamental Units. — All phjrsical quantities, such gs 
force, velocity, etc., can be expressed in terms of the threa 
fundamental quantities : Im^^^^ mass, and /tmg. Each of thecs 
quantities must be measured in terms of its own units. 

The system of units, adopted by almost universal consent, 
and used throughout these Lessons, is the so-called "Centi- 
metre-Gramme-Second" system, in which the fundamental 
units are : — 

The Centimetre as a unit of length ; 

The Gramme as a unit of mass ; 

The Second as a unit of thne. 

The Centimetre is equal to 0*3937 inch in length, and no- 
minally represents one thousand-millionth part, or fTo^oTo^D.T^o 
of a quadrant of the earth. 

The Metre is loo centimetres, or 39*37 inches. 

The Kilometre is 1 000 metres, or about 1093*6 yards. 

The Millimetre is the tenth part of a centimetre, or 0*03937 
inch. 

The Gramme is equal to 15*432 grains, and represents the 
mass of a cubic centimetre of water at 4** C : the Kilogramme is 
1000 grammes or 2*2 pounds. 

255. Derived Units. — 

Area. — The imit of area is the square centimetre. 

Volume. — The unit of volume is the cubic centimetre. 

Velocity. — The imit of velocity is the velocity of a bou) 
which moves through unit distance in unit time, or the 
velocity of one centimetre per second. 

Acceleration. — The unit of acceleration is that acceleration 
which imparts unit velocity to a body in unit time, or 
an acceleration of one centimetre -per -second per second. 
The acceleration due to gravity imparts in one second 
a velocity considerably greater than this, for the velocity 
it imparts to falling bodies is about 981 centimetres per 



JHAP. IV.] ELECTRICITY AND MAGNETISM. 209 

second (or about 32*2 feet per second). The value differs 
slightly in different latitudes. At Bristol the value of 
the acceleration of gravity is ^ = 981*1 ; at the Equator 
g =s 978*1 ; at the North Pole g = 983 'l. 

Fof-ce^ -The unit of force is that force which, acting for one 
second on a mass of one gramme, gives to it a velocity 
of one centimetre per second. It is called one Dyne, 
The force with which the earth attracts any mass is 
usually called the ''weight" of that mass, and its value 
obvioUwty differs at different points of the earth's surface. 
The force with which a body gravitates, i,e, its weight 
(in dynes), is found by multiplying its mass (in grammes) 
by the a alue of g at the particular place where the force 
is exerted. 

Work, — The unit of work is the work done in overcoming 
unit force through unit distance, i.e. in pushing a body 
through a distance of one centimetre against a force of 
one dyne. It is called one Erg. Since the "weight" 
of one gramme is I x 981 or 981 dynes, the work of 
raising one gramme through the height of one centimetre 
against the force of gravity is 98 1 ergs. 

Energy, — The unit of energy is also the erg ; for the energy 
of a body is measured by the work it can do. 

Heat, — The unit of heat (sometimes called a calorie) is the 
amount of heat required to warm one gramme mass of 
water fiom 0° to i° (C) ; and the dynamical equivalent 
of this amount of heat is 42 million ergSy which is the 
value of .Joule's equivalent, as expressed in absolute 
(C.G.S.) measure. {See also Art. 367.) 

Tliese units are sometimes called " absolute " units ; the term absolute, 
introduced by Gauss, meaning that they are independent; of the size of any 
particular instrument, or of the value of gravity at any particular place, or of 
any other arbitrary quantities than the three standards of length, mass, and 
time. It is, however, preferable to refer to them by the more appropriate 
name of ** CG.S. units," as being derived from the centimetre, the gramme, 
and the second. 

256. Electrical Units. — There are two systems of electrical 
units derived from the fundamental "C.G.S." units, one set 
being based upon the force exerted between two quantities of 
electricity, and the other upon the force exerted between two 
magnet poles. The former set are termed electrostatic units, the 
latter electromagnetic units. The important relation between the 
two sets is explained in th« note at the end of Lesson XXX. 

P 



^16 ELEMENTARY LESSONS ON [chap. iV. 

257. Electrostatic Units. — No special names have been 
assigned to the electrostatic units of Quantity, Potential, 
Capacity, etc. The reasons for adopting the following values 
as units are given either in Chapter I. or in the present Chapter. 

Unit of Quantity, — The unit of quantity is that quantity of 
electricity which, when placed at a distance of one 
centimetre (in mx) from a similar and equal quantity, 
repels it with a force of one dyne (Art. 236), 

Potential, — Potential being measured by work done in moving 
a unit of + electricity against the electric forces, the unit 
of potential will be measured by the unit of work, the erg. 

Unit Difference of Potential, — Unit difference of potential 
exists between two points, when it requires the expendi- 
ture of one erg of work to bring a unit of + electricity 
from one point to the other against the electric force 
(Art. 242). 

Unit of Capacity, — That conductor possesses unit capacity 
which requires a charge of one unit of electricity to bring 
it up to unit potential. A sphere of one centimetre 
radius possesses unit capacity (Art. 247). 

Specific, Inductive Capacity is defined in Art. 268 as the ratio 
between two quantities of electricity. The specific- 
inductive capacity of the air is taken as unity. 

258. Dimensions of CJnits. — It has been assumed above 
that a ^ elocity can be expressed in centimetres per second ; for 
velocity is rate of change of place, and it is clear that iT change 
of place may be measured as a length in centimetres, the rate 
of change of place will be measured by the number of centir 
metres through which the body moves in unit of time. It is 
impossible, indeed, to express a velocity without regarding it as 
the quotient of a certain number of units of length divided by 
a certain number of units of time. In other words, a velocity 

= -^^?^y \ or, adopting L as a symbol for length, and T as' a 
symbol for time, V = t, which is still more conveniently written 
V = LxT'". ina. similar way ctcceleration being rate of 
change of velocity, we have A = ijr = ;;r^ = x^ = L x T "" ' 

Now these physical quantities, "velocity," and "acceleration," 
are respectively always quantities of the same nature, no matter 
whether the centimetre, or the inch, or the mile, be talc en as the 
uuit of length, or the second or any other interval be taken as 



CHAP, iv.l ELECTRICITY AND MAGNETISM. 



211 



the unit of time. Hence we say that these abstract equations 
express the ^^ dimensions^'* of those quantities with respect to the 
fundamental quantities length and time. A little consideration 
will show the student that the following will therefore be the 
dimensions of the various imits mentioned above : — 





Units. 


Dimensions. 


/ 

m 
t 

a 
f 


{Fundametital, ) 

Length 

Mass 

Time 


L 

M 
T 


{Derived. ) 

Area = L x L ea 
Volume = L X L X L = 
Velocity = L -e- T « 
Acceleration = velocity -f- time = 
Force = mass x acceleration = 
Work = force- x length = 


LT-^ 

LT-^ 
MLT"" 
ML- T""\ 


i 

V 

R 
C 
k 


{Electrostatic.) 


m^lIt-^ 

M^L^T-' 

M* L* t " ^ 

L-^T^ 

L 
a numeral 

MiL^T""^ 


Quantity = Vforce X (distance) 2 = 

Current = quantity -^ time = 
Potential - work -r- quantity = 

Resistance = -potential — current = 
Capacity = quantity •— potential = 
Sp. Ind. Capacity = quantity -~ another quantity 
Electromotive Intensity = force -f- quantity = 



The dimensions of magnetic units are given in the note on 
Magnetic Units, Art, 324. 

Lesson XXL — Electrometers, 

Q59. In Lesson II. we described a number oi electro- 
scopes or instruments for indicating the presence and 



212 ELEMENTARY LESSONS ON [chap, iv 

sign of a charge of electricity ; some of these also served 
to indicate roughly the amount of these charges, but none 
of them save the torsion balance could be regarded as 
affording an accurate means of measuring either the 
quantity or the potential of a given charge. An instru- 
ment/or 7neasuring differ e7ices of electrostatic potential is 
termed an Electrometer. Such instruments, can also 
be used to measure electric quantity indirectly, for the 
quantity of a charge can be ascertained by measuring 
the potential to which it can raise a conductor of known 
capacity. The earliest electrometers attempted to measure 
the quantities directly. Lane and Snow Harris constructed 
" Unit Jars " or small Leyden jars, which, when it was 
desired to measure out a certain quantity of electricity, 
were charged and discharged a certain number of times. 
The discharging gold-leaf electroscope of Gaugain was 
invented with a similar idea. 

260. Repulsion Electrometers. — The torsion 
balance, described in Art. 15, measures quantities by 
measuring the forces exerted by the charges given to the 
fixed and movable balls. It can only be applied to the 
measurement of repelling forces, for the equilibrium is 
unstable in the case of a force of attraction. 

There are, besides the gold-leaf electroscope and the 
Lane's electroscope, described in Lesson XL, a number 
of finer electrometers based upon the principle of repul- 
sion, some of which resemble the torsi<ni balance in 
having a movable ^rm turning about a central axis. 
Amongst these are the electrometers of Dellmann and of 
Peltier ; the latter of these is shown in Fig. 1 1 1, in the 
Lesson on Atmospheric Electricity. In this apparatus a 
light arm of aluminium, balanced upon a point, carries 
also a small magnet to direct it in the magnetic meridian. 
A fixed arm, in metallic contact with the movable one, 
also lies in the magnetic meridian. A charge imparted 
to this instrument produces a repulsion between the fixed 
and movable arms, causing an angular deviation. Here, 



CHAP, iv.j ELECTRICITY AND MAGNETISM. 213 

however, the force is measured not by being pitted against 
the torsion of an elastic fibre, or against gravitation, but 
against the directive magnetic force of the earth acting 
on the small needle. Now this depends on the intensity 
of the horizontal component of the earth's magnetism at 
the place, on the magnetic moment of the needle, and 
on the sine of the angle of its deviation. Moreover, the 
repulsion here is not between two charges collected on 
small spheres, but between the fixed arm and the mov- 
able one. Hence, to obtain quantitative values for the 
readings of this electrometer, it is necessary to make 
preliminary experiments and to " calibrate " the degree- 
readings of the angular deviation to an exact scale. 

261. Attracted - Dlso Electrometers. — Snow 
Harris was the first to construct an electrometer for 
measuring the attraction between an electrified and a 
non-electrified disc; and the instrument he devised may 
be roughly described as a balance for weighing a charge 
of electricity. More accurately speaking, it was an 
instrument resembling a balance in form, carrying at one 
end a light scale pan ; at the other a disc was hung 
above a fixed insulated disc, to which the charge to be 
measured was imparted. The disadvantages of this 
instrument were manifold, the chief objection being due 
to the irregular distribution of the charge on the disc. 
The force exerted by an electrified point falls off inversely 
as the square of the distance, since the lines of force 
emanate in radial lines. But in the case of a uniformly 
electrified plane surface, the lines of force are normal to 
the surface, and parallel to one another ; and the force 
is independent of the distance. The distribution over 
a small sphere nearly fulfils the first of these conditions. 
The distribution over a flat disc would nearly fulfil the 
latter condition, were it not for the perturbing effect of 
the edges of the disc where the surface-density is much 
greater (see Art. 35); for this reason Snow Harris's 
electrometer was very imperfect. 



214 



ELEMENTARY LESSONS ON [chap. iv. 



Sir W. Thomson has introduced several very import- 
ant modifications into the construction of attracted-disc 
electrometers, the chief 'of these being the employment 
of the " guard-plate " and the providing of means for 
working v/ith a definite standard of potential. It would 
be beyond the scope of these lessons to give a complete 
description^ of all the various forms of attracted-disc 
electrometer ; but the main principles of them all can be 
readily explained. 

The disc. C, whose attraction is to be measured, is sus- 
pended (Fig. I go) within a fixed guard-plate, B, which 




Fig. lOQ. 



surrounds it without touching it, and which is placed 
in metallic contact with it by a fine wire. A lever, L, 
supports the disc, and is furnished with a counterpoise ; 
whilst the aluminium wire which serves as a fulcrum may 
be also employed to produce a torsion force. In order 
to know whether the disc is precisely level with the 
lower surface of the guard-plate a little gauge or index 
is fixed above, and provided with a lens, /, to observe 
its indications, Beneath the disc and guard-plate i^ 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 215 

a second disc, A, supported on an insulating stand. This 
lower disc can be raised or lowered at will by a micro- 
meter screw, great care being taken in the mechanical 
arrangements that it shall always be parallel to the 
plane of the guard -plate. Now, since the disc and 
guard-plate are in metallic connection with one another, 
they -form virtually part of one surface, and as the 
irregularities of distribution occur at the edges of the 
surface, the distribution over the surface of the disc is 
practically uniform. Any attraction of the lower plate 
upon the disc might be balanced either by increasing 
the weight of the counterpoise, or by putting a torsion 
on the wire ; but in practice it is found most convenient 
to obtain a balance by altering the distance of the lower 
plate until the electric force of attraction exactly 
balances the forces (whether of torsion or of gravity 
acting on the counterpoise) which tend to lift the disc 
above the level of the guard-plate. 

The theory of the instrument is simple also. The 
force F just outside a charged conductor is 47r/o (Art. 
252); and since electric force is the same thing as 
the rate of change of potential per unit of length 
(Art. 241), it will be equal to g, where V is the 
difference of potentials between the upper and lower 
plates, and D the distance between them : hence p = — =: . 

If the surface of the movable disc be S, the quantity of 
the charge on it will be Sp. Now, let us suppose that 
the electricity on 'the lower plate has an equal denisity 
but of opposite sign, as will be the case if either plate is 
connected to ** earth." Since its density is — p it will 
exercise a force of — 21: p on a -f- unit placed near the disc ; 
(but as this force is a force exerted from the upper side 
of the plate we must change its sign again and call it 
+ 27r/o, where the -h sign signifies a force tending to 
move a + unit downwards,) Now on the ^isc there are 



2i6 ELEMENTARY LESSONS ON [CHAP. iv. 



Sp units of e.ectricity ; hence the total force of attraction 
on the disc will be F = 2'n-p xSp. 



whence V 



=V¥- 



From this we gather that, if the force F remain the 
same throughout the experiments, //le difference of po- 
tentials between the discs will be simply proportional to 
the distance between them when the disc is in . level 

equilibrium. And the quantity. /?^ may be deter- 
mined once for all as a "constant" of the instrument; 

In the more elaborate forms of the instrument, such 
as the "absolute electrometer," and the "portable 
electrometer," the disc and guard -plate are covered 
with a. metallic cage, and are together placed in com- 
munication with a condenser to keep them at a known 
potential. This obviates having to make measurements 
with zero readings, for the differences of potential will 
now be proporiional to differences of micro7neier readings^ 

or, V,-V,= (D,-D,)^/§|F. 

The condenser is provided in these instruments with 
a gauge^ itself an attracted-disc; to indicate when it is 
charged to the right potential, and with a reple7tisher to 
increase or decrease the charge, the replenisher being 
a little convection-induction machine (see Art. 4 5). 

262. Tlie Quadrant Electrometer. — The Quad- 
rant Electrometer of Sir W. Thomson is an example oi 
a different class of electrometers, in which use is made 
of an auxiliary charge of electricity previously imparted 
to the needle of the instrument. The needle, which con- 



riiAP. IV.] ELECTRICITY AND MAGNETISM. 217 



sists of a thin flat piece of metal hung horizontally by a 
fibre or thin wire, thus charged with, say, + electricity, 
will be attracted by a - charge, but repelled by a + 
charge ; and such attracHon or repulsion will be stronger 
in proportion to these charges, and in proportion to the 
charge on the needle. Four quadrant -pieces of brass 
are fixed horizontally below the needle without touching 
it or one another. Opposite Quadrants are joined with 
fine wires. 

Fig. 1 01 shows a very simple form of the Quadrant 
Electrometer, as arranged for qualitative experiments. 



Fig. 



The four quadrants are enclosed within a glass case, and 
the needle, which carries a light mirror, M, below ^t| is 
suspended from a torsion, head, C, by a very thin metallic 
wire, F. It is electrified to a certam potential by being 
connected, through a wire attached to C, with a charged 



2l8 ELEMENTARY LESSONS ON [chap. I v. 

Leyden jar or other condenser. In order to observe 
the minutest motions of the needle, a reading-telescope 
and scale are so placed that the observer looking through 
the telescope sees an image of the zero of the scale 
reflected in the little mirror. The wires connecting 
quadrants i and 3, 2 and 4, are seen above the top of 
the case. The needle and quadrants are shown in plan 
separately above. If there U the slightest difference of 
potential between the pairs of quadrants, the needle, 
which is held in its zero position by the elasticity of the 
wire, will turn, and so indicate the difference of potential. 
When these deflections are small, the scale readings will 
be very nearly proportional to the difference of potential. 
The instrument is sufficiently delicate to show a difference 
of potential between the quadrants as small as the ^ of 
that of the DanielPs cell. 

For very exact measurements many additional refine- 
ments are introduced into the instrument. Two sets of 
quadrants are employed, an upper and a lower, having 
the needle between them. The torsion wire is replaced 
by a delicate bifilar suspension (Art. 118). To keep 
up the charge of the Leyden jar a " Replenisber " is 
added ; and an " attracted-disc," like that of the Absolute 
Electrometer, is employed in order to act as a gauge to 
indicate when the jar is charged to the right poterAtial. 
In these forms the jar consists of a glass vessel placed 
below the quadrants, coated externally with strips of tin- 
foil, and containing strong sulphuric acid which serves 
the double function of keeping the apparatus dry by 
absorbing the moisture and of acting as an internal 
coating for the jar. It is also more usual to throv/ a 
spot of light from a lamp upon a scale by means of the 
little mirror (as described in the case of the Mirror 
Galvanometer, in Art. 202), than to adopt the subjective 
method with the telescope, which only one person at a_ 
time can use. When the instrument is provided with 
replenisher and gauge, the measurements can be made in 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 219 

tenns of absolute units, provided the *^ constant " of the 
particular instrument (depending on the suspension of 
the needle, si-'e and position of needle and quadrants, 
potential of the gauge, etc.) is once ascertained. 

263. Aa example will illustrate the mode of using the instru- 
ment. It is known that when the two ends of a thin vnre are 
kept at two different potentials a current flows through the wire, 
and that if the potential is measured at different points along 
the wire, it is found to fall off in a perfectly uniform manner 
from the end that is at a high potential down to that at the low 
potential. At a point one quarter along the potential \\'iil have 
fallen off one quarter of the whole difference. This could be 
proved by joining the two ends of the wire through which the 
current was flowing to the terminals of the Quadrant Electro- 
meter, when one pair of quadrants would be at the higL 
potential and the other at the low potential. The needle would 
turn and indicate a certain deflection. Now, disconnect one of 
the pairs of quadrants from the low potential end of the wire, 
and place them in communication with a point one quarter 
along the wire from the high potential end. The needle will 
at once indicate that the difference of potential is but one quarter 
of what it was before. 

Often the Quadrant Electrometer is employed simply as a 
very delicate clecixoscoJ>a in systems of measurement in which a 
difference of electric potential is measured by being balanced 
against an equal and opposite difference of potential, exact 
balance being indicated by there being no deflection of the 
Electrometer needle. Such methods of experimenting are known 
as ^^ Null Methods,'' or '^ Zero Methods:' 

264. Dry-Pile Electrometer. — The principle of 
symmetry observed in the Quadrant Electrometer was 
previously employed in the Electroscope of Bohnenberger 
— a much less accurate instrument — in which the charge 
to be examined was imparted to a single gold leaf, placed 
symmetrically between the poles of a dry-pile (Art 182)5 
toward one or other pole of which the leaf was attracted. 
Fechner modified the instrument by connecting the + 
pole of the dry-pile with a gold leaf hanging between 
two metal discs, from the more ^ of which it was re^ 



220 ELEMENTARY LESSONS ON fCHAP. iv. 

pelled. The inconstancy of dry -piles as sources of 
electrification led Hankel to substitute a battery of a 
very large number of small DanielPs cells. 

265. Capillary Electrometers, — The Capillary 
Electrometer of Lippmann, as modified by Devvar, was 
described in Art. 225. 



Lesson XXII. — Specific Inductive Capacity^ etc. 

266. In Lesson VI. it was shown that the capacity 
of a Leyden jar or other condenser depended upon the 
si/e of the conducting coatings or surfaces, the thinness 
of the glass or other dielectric between them, and upon 
the particular " inductive capacity " of the dielectric 
used. We will now examine the subject in a more 
rigorous way. In Art. 246 it was laid down that the 
capacity of a conductor was measured by the quantity 
of electricity required to raise its potential to un^ity ; or 
if a quantity of electricity Q raise Ihe potential from 
V to V then its capacity is 



Now, a Leyden jar or other condenser maj be 
regarded as a conductor, in which (owing to the parti- 
cular device of bringing near together the two oppositely- 
charged surfaces) the conducting surface can be made 
to hold a very large quantity of electricity without its 
potential (whether + or — ) risking very high. The 
capacity of a condenser, like that of a simple con- 
ductor, will be measured by the quantity of electricity 
required to produce nnii rise of potential. 

267. Theory of Spherical Air - Condenser. —• 
Suppose a Leyden jar made of two concentrit' i^^tal 
sphereo, one inside the other, the space betweer them 
being filled by air. The inner one, A, wiU represent the 
interior coating of tinfoil, and the outer sphere, B (Fig. 



CHAP. iv.J ELECTRICITY AND MAGNETISM. 



221 



102), will represent the exterior coating. Let the radii 

of these spheres be r and / 

respectively. Suppose a charge 

of Q units to be imparted 

to A; it will induce on the 

inner side of B an equal 

negative charge — Q, and to 

the outer side of B a charge 

+ Q will be repelled. This 

latter is removed by contact 

with "earth," and need be 

no further considered. The 

potential^ at the centre M, 

calculated by the rule given 

in Art. 238, will be 

ir _ Q Q 
^ M - - ~ 7 

At a point N, outside the outer sphere and quite near to 
it, the potential wdll be the same as if these two charges, 
+ Q and - Q, were both concentrated at M. Hence 

40-9 




Fig, loa 



y^ = 



o. 



v^* 



So then the difference of potentials will be 
whence ^-^-^ = '^. 

Vai - Vjr y -r 

But, by the preceding Article, the capacity K 
therefore K= ~. 

We see from this formula that the capacity of the 
condenser is proportional to the size of the metal globes, 
and that if the insulating layer is very thin, — that is, if 
r be very nearly as great as r', r* -^r will become very 

1 The student must remember that as there is no electric force within a 
closed conductor the potential at the middle is just the same as at any other 
point inside ; so that it is somewhat a stretch of lang^uage to talk ef tho 
middle point M as having a potential. 



222 ELEMENTARY LESSONS ON [chap, iv 

small, and the value of the expression — ^ will become 
very great ; which proves the statement that the capacity 
of a condenser depends upon the thinness of the layer 
of dielectric^ 

268. Specific Inductive Capacity. — Cavendish 
was the first to discover that the capacity of a condenser 
depended not on its actual dimensions only, but upon 
the inductive power o( Xh^ material used as the dielectric 
between the two surfaces. If two condensers (of any of 
the forms to be described) are made of exactly the same 
size, and in one of them the dielectric be a layer of air, 
and in the other a layer of some other insulating sub- 
stance, it is found that equal quantities of electricity 
imparted to them do not produce equal differences -of- 
potentials ; or, in other words, it is found that they have 
not the same capacity. If the dielectric be sulphur, 
for example, it is found that the capacity is about three 
times as great ; for sulphur possesses a high inductive 
power and allows the transmission -across it of electro- 
static influence three times as well as air does. The 
name specific inductive capacity^ was assigned by 
Faraday to the ratio between the capacities of two con- 
dehsers equal in size, one of them being an air-condenser, 
the other filled with the specified dielectric. The 
specific inductive capacity of dry air at the temperature 
o** C, and pressure 76 centims., is taken as the standard 
and reckoned as unity. 

Cavendish, about the year 1775, measured the specific 
inductive capacity of glass, bees -wax, and other sub- 
stances, by forming them into condensers between two 
circular metal plates, the capacity of these condensers 
being compared with that of an air condenser (resem- 
bling Fig. 30) and with other condensers which he 

1 The name is not a very happy ont,^-^s^eci/t<: inducHvity would haVe been 
better, and is the analogous term, fbr dielectrics, to the term *' specific con- 
ductivity " used for conductors. The term dielectric capacity is also used by 
some modem writers. 



CHAr. IV.] ELECTRICITY AND MAGNETISM. 



223 



called ^^trial-plates." He even went so far as to com- 
pare the capacities of these " trial-plates " with that of a 
sphere of I2| inches diameter hung up in the middle of 
a room. 

269, Faraday's Experiraents. — In 1837 Faraday, 
who did not know of the then un- 
published researches of Caven- 
dish, independently discovered 
specific inductive capacity, and 
measured its value for several 
substances, using for this pur- 
pose tv/o condensers of the form 
shown in Fig. 103. Each 
consisted of a brass ball A, 
enclosed inside a hollow sphere 
of brass B, and insulated 
by a long plug of shellac, up 
which passed a wire terminating 
in a ball a. The outer sphere 
consisted of two parts which 
could be separated from each 
other in order to fill the hollow 
space with any desired material : 
the experimental process then 
was to compare their capacities 
when one was filled with the 
substance to be examined, the 
other containing only dry air. 
The method of experimenting 
was simple. One of the condensers was charged with 
electricity. It was then made to share it3 charge with the 
other condenser, by putting the two inner coatings into 
metallic communication with one another, the outer 
coatings also being in communication with one another. 
If their capacities were equal they would share the charge 
equally, and the potential after contact would be just 
half what it was in the charged condenser before con- 




Fig. 103. 



224 ELEMENTARY LESSONS ON [chav. iv. 

tact. If the capacity of one was greater than the other 
the final potential would not be exactly half the original 
potential, because they would not share the charge 
equally, but in proportion to their capacities. The 
potentials of the charges were measured before and 
after contact by means of a torsion balance. ^ Faraday's 
results showed the following values: — Sulphur, 2*26: 
shellac, 2*0; glass, 176 or more. 

270. Recent Researches. — Since 1870 large addi- 
tions to our knowledge of this subject have been made. 
Gibson and Barclay measured the inductive capacity of 
paraffin by comparing the capacily of an air condenser 
with one of paraffin by means of a sliding condenser, and 
a divided condenser called a ** platymeter,'* using a 
quadrant electrometer as a sensitive electroscope to 
adjust the capacity of the condensers exactly to equality. 
Wiillner, Boltzmann, and others, have also examined 
the inductive capacity of solid bodies by several methods. 
Hopkinson has examined that of glass of various kinds, 
using a constant battery to produce the required differ- 
ence of potentials, and a condenser provided with a 
guard -ring for a purpose similar to that of the guard- 
ring in absolute electrometers. Gordon has still more 
recently made a large number of observations, using a 
delicate apparatus known as a statical " induction 
balance," which is a complicated condenser, so arranged 
in connection with a ^quadrant electrometer that when 
the capacities of the separate parts are adjusted to 
equality there shall be no deflection in the electrometer, 
whatever be the amount or^ign of the actual electrifi- 

1 The value of tlie specific inductive capacity ^! could then be calculated 
as follows : — 

Q==VK = V'fe + V'K/& 

(where K is the capacity of the first apparatus and V its potential, and V' 
the potential after communication with the second apparatus, whose 
capacity isK^): 

hence V = V (i -f- it) 

and ^ = ^^;^' 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 



225 



cation employed, for the moment. This arrangement, 
when employed in conjunction with an induction coil 
(Fig. 148) and a rapid commutator, admits of the in- 
ductive capacity being measured when the duration of 
the actual charge is only very small, the electrification 
being reversed 1 2,000 times per second. Such an instru- 
ment, therefore, overcomes one great difficulty besetting 
these measurements, namely, that owing to the apparent 
absorption of part of the charge by the dielectric (as 
mentioned in Arf. 53), the capacity of the substance, 
when measured slowly, is different from its <* instantane- 
ous capacity." This electric absorption is discussed 
further in Art. 272. The amount of the absorbed charge 
is found to depend upon the time that the charge has 
been accumulated. For this reason the values assigned 
by different observers for the inductive capacity of various 
substances differ to a most perplexing degree, especially 
in the case of the less perfect insulators. The following 
Table summarises Gordon's observations : 



Air . 


i-oo 


Glass . . , 


. 3013 


Ebonite 


2-284 


Guttapercha 


2-462 


Indiarubber 


2-220 


Paraffin (solid) . 


. . I -993^ 


Shellac 


274 


SulJ)hur 


. . 2-58 



to 3-258 



to 2*497 



Gordon's values would probably have been more 
reliable had the plates of*-the induction balance been 
provided with guard-rings' (Art. 248). Hopkinson, 
whose method was a ^' slow " one, found for glass 
much higher inductive capacities, ranging from 6-5 to 
ID- 1, the denser kinds having higher capacities. Row- 
land has lately examined the Inductive capacity of 
plates of quartz cut from a homogeneous crystal, and 
find^ it perfectly devoid of electric absorption. Caven- 
dish obse^pd that the ^apparent capacity of glass 



226 



ELEMENTARY I/ESSONS ON [chap, iv 



became much greater at those temperatures at which it 
begins to conduct electricity. Boltzmann has announced 
that in the case of two crystalline substances, Iceland 
spar an3 sulphur, the inductive capacity is different in 
different directions, according to their position' with 
respect to the axes of crystallisation. 

271. Specific Inductive Capacity of Liquids 
and Gases. — The inductive capacity of liquids also 
has specific values. The following table is taken from 
the data of Silow and of Gordon : — 



Turpentine . 
Petroleum . 
Bisulphide of Carbon 



2'l6 

2*03 to 2 '07 

i-8i 



Faraday examined the inductive capacity of several 
gases by means of his apparatus (Fig. 103), one of the 
condensers being filled with air, the other with the gas 
which was let in through the tap below the sphere after 
exhaustion by an air pump. The method was too rough, 
however, to enable him to detect any difference between 
them, although many experiments, were made with dif- 
ferent pairs of gases at different temperatures and under 
varying pressures. More recently Boltzmann, and inde- 
pendently Ayrton and Perry, have measured the specific 
inductive capacities of different gases by very exact 
methods ; and their results agree very fairly. 





Boltzmann. 


Ayrton and Perry. 

(I) 


Air . 


(1) 


Vacuum . , . . 


(0-999410) 


(0-9985) 


Hydrogen 


0-999674 


0-9998 


Carbonic Acid . 


1 -000356. 


1-0008 


defiant Gas . 


I -00072:2 




Sulphur Dioxide 




10037 



272. Mechanical Effects of Dielectric Stress. 
-Thai different insulating substances have specific 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 227 

inductive power sufficiently disproves the idea that 
induction is merely an " action at a distance," for it is 
evident that the dielectric medium is itself concerned in 
the propagation of induction, and that some media allow 
induction to take place across them better than others. 
The existence of a residual charge (Art. 53) can be 
explained either on the supposition that the dielectric is 
composed of heterogenous particles which have unequal 
conducting powers, as Maxwell has suggested, or on the 
hypothesis that the molecules are actually subjected to 
a strain from which, especially if the stress be long-con- 
tinued, they do not recover all at once. Kohlrausch and 
others have pointed out the analogy between this pheno- 
menon and that of the "elastic recovery" of solid bodies 
after being subjected to a bending or a twisting strain. 
A fibre of glass, for example, twisted by a certain force, 
flies back when released to almost its original position, 
a slight sub -permanent set remains, from which, how- 
ever, it slowly recovers itself, the rate of its recovery 
depending upon the amount land duration of the original 
twisting strain. Hopkinson has shown that it is possible 
to superpose several residual charges, even charges of 
opposite signs, which apparently " soak out " as the 
strained material gradually recovers itself. Perry and 
Ayrton have also investigated the question, and have 
shown that the polarisation charges fn voltameters exhibit 
a similar recovery.* Air condensers exhibit no residual 
charges. 

When a condenser is discharged a sound is often heard. 
This was noticed by Sir W. Thomson in the case of air 
condensers ; and Varley even constructed a telephone in 
which the rapid charge and discharge of a condenser 
gave rise to distinct tones. 

^ It would appear, therefore, probable that MaxwelJ's siiggestion of heiejo- 
geneity of structure, as leading to residual electrification at the bounding 
surface of the particles whose electric conductivities differ, is the true 
explanation of the *' residual '* charge. The phenomenon of elastic recovery 
may itself be du« to heterogeneity of structure. 



228 ELEMENTARY LESSONS ON [chap. iv. 




As to the precise nature of the molecular or mechanical 
operations in the dielectric when thus subjected to the 
stress of electrostatic induction, nothing is known. One 
pregnant experiment of Faraday is of great importance, 
by showing that induction is, as he expressed it, " an 
action of contiguous particles." In a glass trough (Fig. 

104), is placed 
some oil of tur- 
pentine, in which 
are put sonie fibres 
of dry silk cut into 

E ^. small bits. Two 

Fig. 104. 

wires pass into 

thef Liquid, one of which is joined to earth, the other 

being- put into connection with the collector of an 

electrical ^ machine. The bits of silk come from all 

parts of- the litjuid and form a chain of particles from 

wire to wire. On touching them with a glass rod they 

resist being pushed aside, though they at once disperse 

if the supply of electricity is stopped, Faraday regarded 

this as typical of the internal actions in every case of 

induction across a* dielectric, the particles of which he 

supposed to be "polarised," that is, to be turned into 

definite positions, each particle having a positive and a 

negative end. The student will perceive an obvious 

analogy, therefore, between the condition of the particles 

of a dielectric across which electrostatic induction is 

taking place, and the molecules of a piece of iron or 

steel when subjected to magnetic induction. 

Siemens has shown that the glass of a Leyden jar is 
sensibly warmed after being several times rapidly charged 
and discharged. This obviously implies that molecular 
movement accompanies the changes of dielectric stress. 

273. Electric Expansion. — Fontana noticed that 
the internal volume of a Leyden jar increased when it 
was charged. Volta sought to explain this by suggesting 
that the attraction between the two charged surfaces 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 229 

compressed the glass and caused it to expand laterally. 
This idea had previously occurred to Priestley. Dutei 
showed that the amount of apparent expansion was 
inversely proportional to the thickness of the glass, and 
varied as the square of the potential difference. Quincke 
has recently shown that though glass and some other 
insulators exhibit electrical expansion, an apparent con- 
traction is shown by resins and oily bodies under 
electrostatic stress. He connects with these properties 
the production of optical strain and of double refraction 
discovered by Kerr, (See Lesson on Electro-optics, 
ArtJ 386.) 

274. SuDmarine Cables as Condensera — A 
submarine telegraph cable may act as a condenser, the 
ocean forming the outer coating, the internal wire the 
inner coating, while the insulating layers of guttapercha 
correspond to the glass of the Leyden jar. When one 
end of a submerged cable is connected to, say, the + pole 
of a powerful battery, + electricity flows into it. Before 
any signal can be received at the other end, enough 
electricity must flow in to charge the cable to a consider- 
able potential, an operation which may in the case of 
long cables require some seconds. Faraday predicted 
that this retardation would occur. It is, in actual fact, a 
serious obstacle to signalling with speed through the 
Atlantic cables and others. Professor Fleeming Jenkin 
has given the following experimental demonstration of 
the matter. Let a mile of insulated cable wire be coiled 
up in a tub of .water (Fig. 105), one end, N, being 
insulated. The other end is joined up through a long- 
coil galvanometer, G, to the -f pole of a large battery, 
whose - pole is joined by a wire to the water in the tub. 
Directly this is done, the needle of the galvanometer will 
show a violent deflection, + electricity rushing through it 
into the interior of the cable; and a - charge being 
accumulated on the outside of it where the water touches 
the guttapercha. For perhaps an hour the flow will go 



2ZO 



ELEMENTARY LESSONS ON [chap. iv. 



on, though diminishing, until the cable is fully charged. 
Now remove the battery, and instead join up a and d by 
a wire ; the charge in the cable will rush out through the 




Fig, 105. 



galvanometer, which will show an opposite deflection, and 
the residual charge will continue '' soaking out" for a 
long time. 

Since the speed of signalling, and therefore the 
economical working through a cable, depends upon its 
*< capacity'' as a condenser,^ and since its capacity 
depends upon the specific inductive power of the in- 
sulating substance used, Hooper's compound, which has 
an inductive capacity of only 17, and is cheap, is pre- 
ferred to gutta-percha, which is expensive, and has a 
specific iadhctive capacity as high as 2-46* 

275. Use of Condensers. — To avoid this retarda- 
tign and increase the speed of signalling in cables several 
devices are adopted. Very delicate receiving instruments 
are used, requiring only a feeble cui-rent ; for with the 
feebler batteries the actual charge given to the cable is 
less. In some cases a key is* employed which, after 
every signal,' immediately sends into the cable a charge 
of opposite sign, to sweep out, as it were, the charge left 
behind* In duplex signalling (Lesson XXXIX.) the 

1 The capacity of the ** Direct" Atlantic cable from Ballinskelligs (Ireland) 
to Nova Scotia is 992 microfarads. 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 



231 



resistance and electrostatic capacity of the cable have to 
be met by balancing against them an « artificial cable '' 
consisting of a wire of equal resistance, and k condenser 
of equal capacity. Messrs. Muirhead constructed for 
duplexing the Atlantic Cable a condenser containing 
100,000 square feet (over two acres of surface) of tinfoil 
Such condensers are also occasionally used on telegraph 
lines in single working to avoid earth currents. They 
are constructed by placing sheets of tinfoil between 
sheets of mica or of paraffined paper, alternate sheets of 
foil being connected together. Small condensers pf 
similar construction are used in connection with induc- 
tion coils (Fig. 148). 

276. Practical Unit of Capacity.— Electricians adopt a um^ 
of capacity, termed one farad, based on the system of electro- 
magnetic units. A condenser of one farad capacity would be 
raised to a potential of one volt by a charge of one coulomb of 
electricity.''- In practice such a con- 
denser would be too enormous to be 
constructed. As a practical unit 
of capacity is therefore chosen the 
microfarad, or one millionth of a 
farad ; a capacity about equal to 
that of three miles of an Atlantic 
cable. Microfarad condensers are 
made containing about 3600 square 
inches of tinfoil. Their general form 
is shown in Fig. 106, which re- Fig. 105, 
presents a \ microfarad condenser. 

The two brass pieces upon the ebonite top are connected re- 
spectively with the two series of alternate sheets of tinfoil. The 
plug between them serves to keen the condenser discharged 
when not in use. 

Methods of measunng the capacity of a condenser 
are given in Art. 362. 

277. Formula for Capacities of Conductors 
and Condensers.— -The following formulae give the 

^ See Note on Electromagnetic Units, Art. 321. " 




232 ELEMENTARY LESSOl'TS ON [chap. iv. 



capacity of condensers of all ordinary forms, in electro 
static units : — 

Sphere: (radius = r. See Art. 247). 

C =:r. 

Two Co7icentrtc Spheres: (radii r and /, specific 

inductive capacity of the dielectric = ^). 

rr' 
C = k^ 

Cylinder: (length = /, radius = r). 

2 log^ t 

I'wo Concentric Cylinders : (length = /, specific in- 
ductiA^e capacity of dielectric = k^ internal radius 
= r, external radius = /. 

C = >^ — ^—, 

r 

Circular Disc: (radius = r, thickness negligible). 

Two Circular Discs: (like air condenser, Art. 48, 
radii = r, surface = S, thickness of dielectric = ^, 
its specific inductive capacity = k). 

C = A^^ 

4^. 

or C - J^—^ 

(The latter formula applies to any two parallel discs 
of surface S, whether circular or otherwise, provided they 
are lar^e as compared with the distance between 
them.) 

278. Energy of Discharge of Leyden Jar or 
Condenser. — It follows from the definition of potential, 
given in Art. 237^ that in bringing up one -f unit ot 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 233 

electricity to the potential V, the work done is V ergs. 
This assumes, however, that the total potential V is not 
thereby raised, and on this assumption *he work done 
in bringing up Q units would be QV. If, however, the 
potential is nothing to begin with and is raised to V by 
ttie charge Q, the average potential during the operation 
is only \V ; hence the total work done in bringing up 
the charge Q from zero potential to potential V is ^QV 
ergs. Now, according to the principle of the con- 
servation of energy, the work done in charging a jar 
or condenser with electricity is equal to the work which 
could be done by that quantity of electricity when the 
jar is discharged. Hence a |QV represents also the 
energy of the discharge, where V stands for the- dif- 
ference of potential between the two coatings. 

Since Q = VC, it follows that we may \^ite |QV in 
the form J^. That is to say, if a condenSer of capacity 
C is charged by having a quantity Q of electricity 
imparted to it, the energy of the charge is proportional 
directly to the square of the quantity, and inversely to 
the capacity of the condenser. 

If two equal Ley den jars are charged to the same 
potential, and then their inside and outside coatings are 
respectively joined, their united charge will be the same 
as that of a jar of equal thickness, but having twice the 
amount of surface. 

If a charged Leyden jar is placed— similarly in com- 
munication with an uncharged jar of equal capacity, the 
charge will be shared equally between the two jars, and 
the passage of electricity from one to the other will be 
evidenced by the production of a spark v/hen the 
respective coatings are put into communication. Here, 
however, half the energy of the charge is lost in the 
operation of sharing the charge, for each jar will have 
only ^Q for its charge and JV for its potential ; hence 
the energy of the charge of each being half the product 
of charge and potential will only be one quarter of the 



234 ELEMENTARY LESSONS ON [chap. iv. 

original energy. The spark which passes in the 
operation of dividing the charge is, indeed, evidence of 
the loss of energy ; it is about half as powerful as the 
spark would have been if the first jar had been simply 
discharged, and it is just twice as powerful as the small 
sparks yielded finally by the discharge of each jar after 
the charge has been shared between them. 

The energy of a charge of the jar manifests itself, 
as stated above, by the production of a spark at dis- 
charge ; the sound, light, and heat produced being the 
equivalent of the energy stored up. If discharge is 
effected slowly through a long thin wire of high resistance 
the air spark may be feeble, but the wire may be 
perceptibly heated. A wet string being a feeble con- 
ductor affords a slow and almost silent discharge ; here 
probably the electrolytic conduction of the moisture is 
accompanied by an action resembling that of secondary 
batteries (Lesson XXXVIIL) tending to prolong the 
duration of the discharge. 

279. Charge of Jars arranged in Cascade. — 
Franklin suggested that a series of jars might be 
arranged, the outer coating of one being connected with 
the inner one of the next, the outer coating of the last 
being connected to earth. The object of this arrange- 
r^ent was that the second jar might be charged with the 
electricity repelled from the outer coating of the first, 
the third from that of the second, and so on. This 
"cascade" arrangement, however, is of no advantage, 
the whole charge accumulated in the series being only 
equal to that of one single jar. For if the inner coating 
of the first jar be raised to .V, that of the outer coating 
of the last jar remaining at zero in contact with earth, 
the difference of potential between the outer and inner 
coating of any one jar will be only ■- V, where n is 
number of jars. And as the charge in each jar is equal 
to its capacity C, multiplied by its potential, the charge 
in each will only be - CV, and in the whole n jars the 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 235 

total charge will he n - CV, or CV, or equals the charge 
of one jar of capacity C raised to the same potential V. 

Lesson XXIIL — Phenomena of Discharge. 

280. An electrified conductor may be. discharged in 
at least three different ways, depending on the medium 
through which the discharge .is effected, and varying 
with the circumstances of the discharge. 

281. Disruptive Discharge. — In the preceding 
Lesson it has been shown that induction across a non- 
conducting medium is always accompanied by a mechani- 
cal stress upon the medium. If this stress is very great 
the non-conducting medium will suddenly give way and 
a spark will burst across it. Such a discharge is called 
a ** disruptive " discharge. 

A very simple experiment, carefully considered, will 
set the matter in a clear light. Suppose a brass ball 
charged with + electricity to be hung by a silk spring 
above a metal plate lying on the ground. If we lower 
down the suspended ball a spark will pass between it 
and the plate when they come very near together, and 
the ball will then be found to have lost all its previous 
charge. It was charged with a certain quantity of 
electricity, and as it had, when suspended out of the 
range of other conductors, a certain capacity (numeri- 
cally equal to its radius in centimetres), the electricity 
on it would be at a certain potential (namely = ^), and 
the charge would be distributed with a certain surface 
density all over it. The plate lying on the earth would 
be all the while at zero potential. But when the sus- 
pended ball was lowered down towards the plate the 
previous state of things was altered. In the presence 
of the + charge of the ball the potential^ of the plate 

1 The student must remember that, by the definition of potential in 
Art. 237, the potential at a point is the slim of all the separate quantities of 
electricity near it, divided each by its distance from the point. 



236 ELEMET^TARY LESSONS ON [chap, iv, 

would rise, were it not that, by the action termed 
induction, just enough negative electrification appears on 
it to keep its potential still the same as that of the earth. 
The presence of the induced negative electricity on the 
plate will attract the + electricity of the ball downwards, 
and alter the distribution of the electricity on the ball, 
the surface - density becoming greater at the under 
surface, and less on the upper. The capacity of the 
ball will be increased, and therefore its potential will 
fall correspondingly. The layer of air between the ball 
and the plate is acting like the glass of a Leyden jar. 
The more the ball is lowered down the greater is the 
accumulation of the opposite kinds of electricity on each 
side of the layer of air, and the stress across the layer 
becomes greater and greater, until the limit of the 
dielectric strength is reached ; the air suddenly gives 
way and the spark tears a path across. The greater 
the difference of potential between the two bodies, the 
thickei^ will be the layer which can thus be pierced, and 
the longer will be the spark. 

282. Conductive Discharge. — If the discharge 
takes place by the passage of a continuous current^ 
as when electricity flows through a thin wire from the 
collector of a machine back to the rubbers, or from the 
positive pole of a battery to the negative pole, the opera- 
tion is termed a " conductive " discharge. The laws 
of the conductive discharge are explained in Lessons 
XXIX. and XXX. 

283. Oonvective Discharge. — A third kind of 
discharge, differing from either of those above mentioned, 
may take place, and occurs chiefly when electricity of a 
high potential discharges itself at a pointed conductor 
by accumulating there with so great a density as to 
electrify the neighbouring particles of air ; these particles 
then flying off by repulsion, conveying away part of the 
charge with them. Such convective discharges' may 
occur either in gases or in liquids, but are best manl- 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 23) 

Tested in air and other gases at a low pressure/M'n tubes 
exhausted by an air pump. 

The discharge of a quantity of electricity in any of 
the above ways is always accompanied by a transform- 
ation of its energy into energy of some other kind, — 
sound, light, heat, chemical actions, and other pheno- 
mena being produced. These effects must be treated in 
detail 

284. Mechanical Effects. — Chief amongst the 
mechanical effects of the .disruptive spark discharge is 
the shattering and piercing of glass and other insulators. 
The dielectric strength of glass, though much greater 
than that of air, is not infinitely great. A slab of glass 
3 inches thick has been pierced by the discharge of a 
powerful induction-coil. The so-called <' toughened" 
glass has a greater dielectric strength than ordinary 
glass, and is more difficult to pierce. A sheet of glass 
may be readily pierced by a spark from a large Leyden 
jar or battery of jars, by taking the following precau- 
tions : — The glass to be pierced is laid upon a block of 
glass or resin, through which a wire is led by a suitable 
hole, one end of the wire being connected with the outer 
coating of the jar, the other being cut off" flush with the 
surface. Upon the upper surface of the sheet of glass 
that is to be pierced another wire is fixed upright, its 
end being exactly opposite the lower wije, the other 
extremity of this wire being armed with a metal knob to 
receive the spark from the knob of the jar or discharger. 
To ensure good insulation a few drops of paraffin oil, or 
of olive oil, are placed upon the glass round the points 
where the wires touch it. A piece of dry wood similarly 
treated is split by a powerful spark. 

If a spark is led through a tightly corked glass tube 
containing water, the tube will be shattered into small 
pointed fragments by the sudden expansion of the 
liquid. 

The mechanical action of the brush discharge at 



238 ELEMENTARY LESSONS ON [chap, iv- 

points is mentioned in Art. 43, and the mechanical 
effects of a current of electricity were described in 
Lesson XIX. 

285. Lullin's Experiment.— If a piece of card- 
board be perforated by a spark between two metal points, 
two curious facts are observed. Firstly^ there is a slight 
burr raised on each side, as if the hole had been pierced 
from the middle outwards. Secondly^ if the two points 
are not exactly opposite one another the hole is found 
to be nearer the negative point. But if the experiment 
is tried under the air pump in a vacuum^ there is no 
such displacement of the hole ; it is then midway 
exactly. 

286. Ohemioal EflFeots.— The. chemical actions 
produced by currents of electricity have been described 
in Lessons XIV. and XVill. Similar actions can be 
produced by the electric spark, and by the silent glow 
discharge (see Art. 290). Faraday showed, indeed, that 
all kinds of electricity from different sources produced <the 
same kinds of chemical actions, and he relied upon this 
as one proof of the essential identity of the electricity 
produced in different ways. If sparks from an electric 
machine are received upon a piece of white, blotting- 
paper moistened v/ith a solution of iodide of potassium, 
brown patches are noticed where the spark has effected 
a chemical decomposition and liberated the iodine. 

When a stream of sparks is passed through moist air 
in a vessel, the air is found to have acquired the property 
of changing to a red colour a piece of paper stained 
blue with litmus. This, Cavendish showed, was due to 
the presence of nitric acid, produced by the chemical 
union of the nitrogen and oxygen of the air. The effect 
is best shown with the stream of sparks yielded by a 
small induction coil (Fig, 148), in a vessel in which the 
air has been compressed beyond the usual atmospheric 
pressure. 

The spark will decompose ammonia gas, and olefiant 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 239 



gas, and it will also cause chemical combination to take 
place with explosion, when passed through detonating 
mixtures of gases. Thus equal volumes of chlorine and 
hydrogen are exploded by the spark. So are oxygen and 
hydrogen gases, when mixed in the proportion of two 
volumes of the latter to one of the former. Even the 
explosive mixture of common coal gas mixed with from 
four to ten times its own volume of common air, can be 
thus detonated. A common experiment with the so- 
called electric pistol consists in filling a small brass vessel 
with detonating gases and then exploding them by a 
spark. The spark discharge is sometimes applied to 
the firing of blasts and mines in military operations, a 
small quantity of fulminating powder being placed in 
the path of the spark to kindle the larger charge of 
gunpowder or other explosive. (See also Art. 370.) 

287. Physiological Effects. — The physiological 
effects of the current have been described in Lesson 
XIX. Those produced by the spark discharge are mo^e 
sudden in character, but of the same general nature. 
The bodies of persons killed by the lightning spark 
frequently exhibit markings of a reddish tint where the 
discharge in passing through the tissues has lacerated or 
destroyed them. Sometimes these markings present a 
singular ramified appearance, as though the discharge 
had spread in streams over the surface at its entry. 

288. Calorific Effects.— ^ The flow -of electricity 
through a resisting medium is in every case accompanied 
by an evolution of heat. The laws of heating due to 
currents are given in Art. 367. The disruptive discharge 
is a transfer of electricity through a medium of great 
resistance and accompanied by an evolution of heat. 
A few drops of ether in a metallic spoon are easily 
kindled by an electric spark. The spark from an electric 
machine, or even from a rubbed glass rod, is hot enough 
to kindle an ordinary gas-jet. In certain districts of 
America, during the driest season of the ^lear, the mere 



240 ELEMENTARY LESSONS ON [chap. iv. 



rubbing of a person's shoes against the carpet, as he 
shuffles across' the floor, generates sufficient electricity to 
enable sparks to be drawn from his body, and he may 
light the gas by a single spark from his outstretched 
finger. Gunpowder can be fired by the discharge of a 
Leyden jar, but the spark should be retarded by being 
passed through a wet thread, otherwise the powder will 
simply be scattered by the spark. 

.The Electric Air" Thermopteter^inwtwitdi by.* Kinr 
nersley,^ serves to investigate the heating powers of the 
discharge. It consists, of a glass vessel enclosing air, 
and communicating with a tube partly filled with water 
or other liquid, in order to observe changes of volume or 
of pressure. Into this vessel are led two metal rods, 
between which is suspended a thin wire, or a filamopt 
of gilt paper ; or a spark can be allowed simply to cross 
between them.. When the discharge passes the enclosed 
air is heated, expands, and causes a movement of the 
indicating column of liquid. Mascart has further de- 
veloped .the instrument by making it self- registering. 
The results of observation with these instruments are 
as follows 2 — The heating effect produced by a given 
charge in a wire of given length is inversely proportional 
to the square of the area of the cross section of the wire. 
The heating effect is greater, the slower the discharge. 
The total heat evolved is jointly proportional to the 
charge, and to the potential through which it falls. In 
fact, if the entire 'energy of the discharge is expended 
in producing heat, and in doing no other kind of work, 
then the heat developed will be the thermal equivalent 

of ^ QV, or will be ^ units of heat, where J repi-e- 

sents the mechanical equivalent of heat/Q i= 42 milllori % 

1 This instrument differs in no essential respect from that devised eIu 5^;" 
years. later by^iliess, to v/hom the instrument is often accredited. Rk>:, 
however, deduced quantitative laws, while Kinncrsley concenied hL.a 
self with qualitative observations, Cnow Harris r.'-i.'^ anticipated Riess ;ii 
s:3veral points of his researches. 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 241 

since 42 x 10^ ergs ~ i gramme- water-degree of heat), 
and Q and V are expressed in C. G. S. units. 

When a po'werful discharge takes place through very 
thin wires, they may be heated to redness, and even 
fused by the heat evolved. Van Marum thus once 
heated 70 feet of wire by a powerful discharge. A 
narrow strip of tinfoil is readily fused by the charge of 
a large Leyden jar, or battery of jars. A piece of gold 
leaf is in like manner volatilised under the sudden heat- 
ing of a powerful discharge ; ahd Franklin utilised this 
property for a rude process of multiplying portraits or 
other patterns, which, being first cut out in card, were 
reproduced in a silhouette of metallic particles on a 
second card, by the device of laying above them a film 
of gold or silver l^af covered again with a, piece of card 
or paper, and then transmitting the charge of a Leyden 
battery through the leaf between the knobs of a universal 
discharger. 

289. Luminous Eflfecta — The luminous effects 
of the discharge exhibit many beautiful and interesting 
variations under different conditions. The spark of the 
disruptive discharge is usually a thin brilliant streak of 
light. When it takes place between two metallic balls, 
separated only by a short interval, it usually appears 
as a single thin and brilliant line. If, however, the 
distance be as much as a few centimetres, the spark 
takes an irregular zig-zag form. In any case its path is 
along the line of least resistance, the presence of minute 
motes of dust floating in the air being quite sufficient to 
determine the zig-zag character. In many cases the 
spark exhibits curious ramifications and forkings, o' 
which an illustration is given in Fig. 107, which is drawr 
of one eighth of the actual size of the spark obtained 
from a Cuthbertson's electrical machine. The discharge, 
from a Leyden jar affords a much brighter, shorter, 
noisier spark than the spark drawn direct from the 
collector of a machine. The length (see Art 291) 



242 ELEMENTARY LilSSONS ON [ckap. iv. 

depends upon the potential, and up6n the pressure and 
temperature of the air in which the discharge takes 
place. The brilliance depends .chiefly upon the quantity 




Fig, 107. 

of electricity discharged. The colour of the spark varies 
with the nature of the metal surfaces between which 
the discharge takes place. Between, copper or silver 
terminals the spark takes a green tint, while between 
iron knobs, it is of a reddish hue. Examination with 
the spectroscope reveals the presence in the spark of the 
rays characteristic of the incandescent vapours of the 
several metals ; for the spark tears away in its passage 
small portions of the metal surfaces, and volatilises 
them. 

290. Brush Discharge: Glow Discharge. — If 
an electric machine is vigorously worked, but no sparks 
be drawn from its collector, a fine diverging brush of 
pale blue Jight can be seen (in a dark room) streaming 
from the brass ball at the end of it farthest from the 
collecting comb : a hissing or crackling sound always 
accompanies this kind of discharge. The brush dis- 
charge consists of innumerable fine twig-like ramifications, 
presenting a form of which Fig. 1 08 gives a fine example. 
The brightness and, size of the brush is increased by 
holding a flat plate of metal a little way from it. With 
a smaller ball, or with a bluntly pointed wire, the brush 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 543 

appears, smaller, but is more disfinct and continuous. 
The brush discharge is larger and more ramified when a 
positive charge is escapine. than wh^n the electrification 




Fig. 108. 

• 

is negative. Wheatstone found by using his rotating 
mirror that the brush discharge is really a series of 
successive partial sparks at rapid intervals. 

If the blunt or rounded conductor be replaced by a 
pointed one, the brush disappears and gives place to a 
quiet and continuous glow Where the electrified particles 
of air are streaming away at the point. If these con- 
vection-streams are impeded the glow may once more 
give place to the brush. Where a negative charge is 
beirfg discharged at a point, the glow often appears to 
be separated from the surface of the conductor by a dark 
space, where the air, without becoming luminous, still 
conveys the electricity. This phenomenon, to which 
Taraday gave the name of the " dark " discharge^ is very 
well seen when electricity is discharged through rarefied 
air and other gases in vacuum tubes. 

291. Lengtli of Sparks. — Roughly speaking, the 



244 ELEMENTARY LESSONS ON lchap. iv. 



length of spark between two conductors increases with 
the difference between their potentials. It is also found 
to increase when the pressure of the air is diminished. 
Riess found the distance to increase in a proportion a 
little exceeding that of the difference of potentials. Sir 
W. Thomson measured by means of an «' absolute elec- 
trometer " (Art. 261) the difference of potential necessary 
to produce a spark discharge between two parallel plates 
at different distances. His precise experiments confirm 
Riess's observation. Thus, to produce a spark at -i of 
a millimetre distance, the difference of potential must be 
27 (arbitrary) units ; at -5 millim. 7-3 units ; at i millim. 
12-6 units; and at 1-5 millims. 17*3 units. De la Rue 
and Miiller have found with their great battery (Art. 174) 
that with a difference of potential of 1000 volts the strik- 
ing distance of the spark was only '0127 centimetres (or 
about irK of ^^ inch), and with a difference of 10,000 
volts only i*369. Their 1 1,000 silver cells gave a spark 
of I '59 centim. (about f of an inch) long. To produce 
a spark one mile long, through air at the ordinary 
pressure, would therefore require a difference of potential 
exceeding that furnished by 1,000,000,000 Daniell's cells! 

The length of the spark differs in different gases, being 
nearly twice as long in hydrogen as in air at the same 
density, and longer in air than in carbonic acid gas. 

In rarefied air the spark is longer. Snow Harris 
stated that the length of spark was inversely proportional 
to the pressure, but this law is not quite correct, being 
approximately true only for pressures between that of 
eleven inches of mercury and that of 30 inches (one 
atmosphere). At lower pressures, as Gordon has lately 
shown, a greater difference of potential must be used to 
produce a spark than that which would accord wfth 
Harris's law. From this it would appear that thin 
layers of air oppose a proportionally greater resistance 
to the piercing power of the spark than thick layers, and 
possess greater dielectric strength. 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 245 

A perfect vacuum is a perfect insulator — no spark will 
cross it. It is possible to exhaust a tube so perfectly 
that none of our electric machines or appliances can 
send a spark through the vacuous space even over so 
short a distance as one centimetre. 

On the other hand a great increase of pressure also 
increases the dielectric strength of air, and causes it to 
resist the passage of a sparfc . Cailletet compressed dry 
air -at 40 to. 50 atmospheres' pressure, and found that 
even the spark of a powerful induction con failed to cross 
z space of '05 centimetre wide. The length of the spark 
(in air), is* also affected by temperature, sparks being 
longer and straigliter througli hot air than through cold. 

Flames and currents of very hot air, su.ch as those 
rising from a red-hot piece of iron, are extremely good 
conductors of electricity, and act eyen better than 
metallic points in discharging a , charged conductor. 
Gilbert showed' that an electrified body placed near a 
flame lost its charge ; and the very readiest way to rid 
the surface of a. charged body of low conducting power 
of a charge imparted to it by friction or otherwise, is to 
pass it througli the aflame of a spirit-lamp. Faraday 
found negative electrification to be thus more easily dis- 
charged than positive. Flames powerfully negatively 
electrified are.' repelled from conductors, though not so 
when positively electrified. Sir W. Grove has shown 
that a current is set up in a platinum wire, one end 
of which touches the tip, and the other the base, of a 
flame. 

292. Discharges in Partial Vacua. — If the dis- 
charge take place in glass tubes or vessels .from which 
the air has been partially exhausted, many remarkable 
and beautiful luminous phenomena are produced.- A com- 
mon form of vessel is the " electric egg " (Fig. 1 50), a 
sort of o\iil bottle that can be screwed to an air-pump, and 
furnished with brass knobs to lead in the- sparks. More 
often ^^ vacuum tubes," such as those manufactured by 



246 ELEMENTARY LESSONS ON [chap. iv. 

the celebrated Geissler, are employed. These are merely 
tubes of thin glass blown into bulbous or spiral forms, 
provided with two electrodes of platinum wire fused into 
the glass, and sealed off after being partially exhausted 
of air by a mercurial air-pump. Of these Geissler tubes 
the most useful consist of two bulbs joined by a very 
narrow tube, the luminous effects being usually more 
intense in the contracted portion. Such tubes are 
readily illuminated by a spark from an electrophorus or 
electric machine; but it is more common to work them 
with the spark of an induction coil (Fig; 148). 

Through such tubes, before exhaustion, the spark passes 
without any unusual phenomena being produced. As 
the air is exhausted the sparks become less sharply 
defined, and widen out to occupy the whole tube, 
becoming pale in tint and nebulous -in form. The 
negative electrode exliibits a beautiful bluish or violet 
glow, separated from the conductor by a narrow dark 
interval, while at the positive electrode a single small 
bright star of light is all that remains. Frequently the 
light breaks up into a set of siricE^ or patches of light of 
a cup-like form, which vibrate to and fro between darker 
spaces. In nitrogen gas the violet aureele glowing 
around the negative pole is very bright, the rest of the 
light being rosy in tint. In oxygen the difference is not 
so marked. In hydrogen gas the tint of the discharge 
is bluish, except where the tube is narrow, where a 
beautiful crimson may be seen. With carbonic acid gas 
the light is remarkably white. Particles of metal are 
torn off from the negative electrode, and projected from 
its surface. The negative electrode is also usually the 
hotter when made of similar dimensions to the positive 
electrode. It is also observed that the light of these 
discharges in vacuo is rich in those rays which produce 
phosphorescence and fluorescence. Many beautiful 
effects are therefore produced by blowing tubes in 
uranium glass, which fluoresces with a fine green light, 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 247 

and by placing solutions of quinine or other fluorescent 
liquids in outer tubes of glass. 

293. Phenomena in High Vacua. — Crookes has 
found that when exhaustion is carried to a very high 
degree, the dark space separating the negative glow 
from the negative pole increases in width ; and that 
across this space electrified molecules are projected in 
parallel paths normally to the surface of the electrode. 
The chief point relied upon for this theory is, that if 
exhaustion be carried to such a high degree that the 
dark space fills the entire tube or bulb, and bodies 
(whether opaque or transparent) be then interposed in 
front of the electrode, sharply defined shadows of these 
bodies are projected upon the opposite wall of the vessel, 
as if they stopped the way for some of the flying mole- 
cules, and prevented them from striking the opposite 
walli Lightly -poised vanes are also driven round if 
placed in the path of the discharge. Holtz has more 
recently produced "electric shadows," by means of dis- 
charges in air at ordinary pressure, between the poles of 
his well-known machine (Fig. 29), the discharge taking 
place between a point and a disc covered with silk, on 
which the shadows are thrown. See Chapter XIV. 

294. Striae.— The sh 'kb or stratlficaHons have been examined 
very carefully by Gassiot. by Spottiswoode, and Ly De la Rue. 
The principal facts hitherto gleaned are as follow : — The striae 
originate at the positive electrode at a certain pressure, and 
become more numerous, as the exhaustion proceeds, up to a 
certain point, when they become thicker and diminish in number, 
until exhaustion is carried to such a point that no discharge will 
pass. The striae are hotter than the spaces between them. The 
number and position of the striae vary, not only with the exhaus- 
tion but with the difference of potentials of the electrodes. When 
stri^ are produced by the intermittent discharges of the induction 
roil, examinadon of them in a rotating mirror reveals that they 
move forward from the positive electrode towards the negative, 

Schuster has recently shown that the discharge of electricity 
through gases is a process resembling that of electrolysis (Art 
418), being accompanied by breaking up of the gaseous mole- 



248 ELEMENTARY LESSONS ON [chap. iv. 

cules and incessant interchanges of atoms between them. The 
production of ozone (Art. 208) and the phenomena noticed at the 
negative electrode (Art. 292) certainly give support to this view. 
The discharges in vacuum tubes are affected by the magnet 
at all degrees of exhaustion, behaving like flexible conductors. 
Under certain conditions also, the discharge is sensitive to the 
presence of a conductor on the exterior of the tube, retreating 
from the side where it is touched. This sensitive state appears 
to be due to a periodic intermittence in the discharge ; an inter- 
mittence or partial intermittence in the flow would also probably 
account for the production of striae. 

295. Electric Oscillations. — Feddersen examined 
the spark of a Leyden jar by means of a rotating mirror, 
and found that instead of being a single instantaneous 
discharge, it exhibited ^ certain definite fluctuations. 
With very small resistances in the circuit, there was a true 
oscillation of the electricity backward and forward for 
a brief time, these alternate partial discharges being 
probably due to the self-induction of the circuit. With 
a certain higher resistance the discharge became con- 
tinuous but not instantaneous. With a still higher 
resistance, the discharge consisted of a series of partial 
intermittent discharges, following one another in the 
same direction. Such sparks when view^ed in the rotating 
mirror showed a series of separate images at nearly 
equal distances apart. The period of the oscillations 
was found to be proportional to the square root of the 
capacity of the condenser. 

296. Velocity of Propagation of Discharge.— 
The earliest use of the rotating mirror to analyse phe- 
nomena of short duration was made by Wheatstone, 
v/ho attempted by this means to measure " the velocity 
of electricity " in conducting wires. What he succeeded 
in measuring was not, however, the velocity of electricity^ 
but the time taken by a certain quantity of electricity 
to fl6w through a conductor of considerable resistance 
and capacity. Viewed, in a rotating mirror, a spark of 

1 This phenomenon of oscillation was predicted from purely theoretical con 
siderations arising out of the equations of self-induction, by Sir W. Thomson 



r.HAP. iv,j ELECTRICITY AND MAGKETISM. 249 

definite duration would appear to be drawn out into an 
elongated streak. Such an elongation was found to be 
visible when a Leyden jar was discharged through a 
copper wire half a mile long ; and when the circuit was 
interrupted at three points, one in the middle and one at 
each end of this wire, three sparks were obtained, which, 
viev/ed in the mirror, showed a lateral displacement, 
indicating (with the particular rate of rotation employed) 
that the middle spark took place ^^^g^ of a second 
later than those at the ends. Wheatstone argued from this 
a, velocity of 288,000 miles per second. But Faraday 
showed that the apparent rate of propagation of a 
quantity of electricity must be affected by the capacity 
of the conductor ; and he even predicted that since a 
submerged insulated cable acts like a Leyden jar (see 
Art. 274), and has to be charged before the potential 
at the distant end can rise, it retards the apparent flow 
of electricity through it. Professor Fleeming Jenkin 
says of one of the Atlantic cables, that, after contact 
with the battery is made at one end, no effect can be 
detected at the other for two -tenths of a second, and 
that then the received current gradually increases, until 
about three seconds afterwards it reaches its maximum, 
and then dies away. This retardation is proportional 
to the square of the length of the cable as well as to 
its capacity and to its resistance ; hence it becomes 
very serious on long cables, as it rieduces the speed 
of signalling. There is in fact no definite assignable 
" velocity of electricity." 

A very simple experiment will enable the student to 
realise the excessively short duration of the spark of a 
Leyden jar. Let a round disc of cardboard painted 
with black and white sectors be rotated very rapidly so 
as to look by ordinary light like a mere gray surface. 
When this is illuminated by the spark of a Leyden jar it 
appears to be standing absolutely still, however rapidly 
it may be turning. A flash of lightning is equally in- 



250 



ELEMENTARY LESSONS OH [chap. IV. 



stantaneous : it is utterly impossible to determine at 
which end the flash begins.^ 

297. Electric Dust-fl^ures. — Electricity may creep 
slowly over the surface of bad conductors. Lichtenberg 
devised an ingenious way of investigating the distribution 
of electricity by means of certain dust -figures. The 
experiment is very easy. Take a charged Leyden jar 
and write with the knob of it upon a cake of shellac 
or a dry sheet of glass. Then sift, through a bit of 





^m^^ 


^^^^fl 


K^ 


1 






'^ 






msamm 


'^.J' A 


;■■■ : *" 


^j 


1 


^ ::--'-'"- 


-'>^-v>i^ 


^fe^- 


' - j_^; '^S: 


Pr 




1 






^t ^^ 


^ 


i 


€m§C- - 




E^ 


3 


■*-^«f _SP 


•"m^" 





Fig. 109,. 

muslin, over the cake of shellac a mixture of powdered 
red lead and sulphur (vermilion and lycopodium powder 
answer equally well). The powders in this process rub 
against one another, the red lead becoming +, the 
sulphur - . Hence the sulphur will be attracted to 
those parts where there is + electrification on the disc, 
and settles down in curious branching yellow streaks like 

1 Sometimes the flash seems to strike downwards from the clouds some- 
times upwards from the earth. This 13 an optical illusion, resulting from the 
unequal sensitiveness to light of different portions of the retina of the eye. 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 



251 



those shown in Fig. 109. The red lead settles down in 
little red heaps and patches where the electrification is 
negative. Fig. no shows the general appearance of 
the Lichtenberg' s figure produced by holding the knob of 




Fig. no. 

the Leyden jar at the centre of a shellac plate that has 
previously been rubbed with flannel, the negative elec- 
trification being attracted upon all sides toward the 
central positive charge. 

Powdered tourmaline, warmed and then sifted over a 
sheet of glass previously electrified irregularly, will show 
similar figures, though not so well defined. 

Breathfigiires can be made by electrifying a coin or 
other piece of metal laid upon a sheet of dry glass, 
and then breathing upon the glass where the coin lay, 
revealing a faint image of it on the surface of the glass. 

298. Production of Ozone. — Whenever. an elec- 
tric machine is worked a peculiar odour is perceived. 
This was formerly thought to be evidence of the existence 



252 ELEMENTARY LESSONS ON [chap, iv 

of an electric "effluvium" or fluid; it is now known to be 
due to the presence of ozone, a modified form of oxygen 
gas. which differs from oxygen in being denser, more 
active chemically,, and in having a characteristic smell. 
The discharge of the Holtz-machine and that of the 
induction coil are particularly favourable to the pro- 
duction of this substance. 

299. Dissipation of Charge. — However well in- 
sulated a charged conductor may be, and however dry 
the surrounding air, it nevertheless slowly loses its 
charge, and in a few days will be found to be completely 
discharged. The rate of loss of charge is, however, not 
uniform. It is approximately proportional to the dif- 
ference of potential between the body and the earth. 
Hence the rate of loss is greater at first than afterwards, 
and is greater for highly charged bodies than for those 
feebly charged. The law of dissipation of charge 
therefore resembles Newton's law of cooling, according 
to which the rate of cooling of a hot body is propor- 
tional to the difference of temperature between it and 
the surrounding objects.' If the potential of the body 
be measured at equal intervals of time it will be found 
to have diminished in a decreasing geometric series ; or 
the logarithms of the potentials at equal intervals of time 
will differ by equal amounts. 

This may be represented by the following equation : 

where V^ represents the original potential and V^ the potential 
after an interval /. Here e stands for the number' 2*71828 . . • 
(the base of the natural logarithms), and p stands for the "co- 
efficient of leakage," which depends upon • the temperature, 
pressure, and humidity of the air. 

The rate of loss is, howtver, greater at negatively 
electrified surfaces than at positive. 

300. Positive and Negative Electrification. — 
The student will not have failed to notice throughout 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 253 



this Lesson frequent differences between the behaviour 
of positive and negative electrification. The striking dis- 
similarity in the Lichtenberg's figures, the displacement 
of the perforation - point in Lullin's experiment, the 
unequal tendency to dissipation at surfaces, the remark- 
able differences in the various forms of brush and glow 
discharge, are all points that claim attention. Gassiot 
described the appearance in vacuum tubes as of a force 
emanating from the negative pole. Crookes's experi- 
ments in high vacua show molecules to be violently 
discharged from the negative electrode, the vanes of a 
little fly enclosed in such tubes being moved from the 
side struck by the negative discharge. Holtz found that 
when funnel-like partitions were fixed in a vacuum tube 
the resistance is much less when the open mouths of the 
funnels face the negative electrode. These matters are 
yet quite unaccounted for by any existing theory of 
electricity. 

The author of these Lessons is disposed to take the following view on tnis 
point : — If electricity be really 07te and not two^ either the so-called positive 
or the negative electrification must be a state in m hich there is ^/^; ^ electricity 
than in the surrounding space, and the other must be a state in which there 
is less» The student was told, in Art. 6, that in the present state of the science 
we do not know for certain whether " positive " electrification is really an 
excess of electricity or a defect. Now some of the phenomena alluded to in 
^-this Article seem to indicate that the so-called "negative" electrification 
really is the state of excess. In particular, the fact that the rate of dissipa- 
tion of charge is greater for negative electrification than for positive, points 
this way ; because the law of loss of charge is the exact counterpart of the 
law of the loss of heat, in which it is quite certain that, for equal dififerences 
of temperature between a body and its surroundings, the rate of loss of heat 
is greater at higher temperatures than at lower ;. or the body that is really 
hotter loses its heat fastest. 



Lesson XXIV. — Atmospheric EledriJiy. 

301. The phenomena of atmospheric electricity are 
of two kinds. There are the well-knov/n electrical pheno- 
mena of thunderstorms ; and there are the phenomena 



254 ELEMENTARY LESSONS ON [chap, iv, 

of continual slight electrification in the air, best observed 
when the weather is fine. The phenomena of the Aurora 
constitute a third branch of the subject. 

302. The Tkunderstorm an Electrical Pheno- 
menon. — The detonating sparks drawn fr«m electrical 
machines and from Leyden jars did not fail to suggest 
to the early experimenters, Hawkesbee, Newton, Wall, 
NoUet, and Gray, that the lightning flash and the thunder- 
clap were due to electric discharges.- in 1749, Ben- 
jamin Franklin, observing lightning to possess almost 
all the properties observable in electric sparks,^ suggested 
that the electric action of points (Art. 43), which was 
discovered by him, might be tried on thunderclouds, 
and so draw from them a charge of electricity. He 
proposed, therefore, to fix a pomted iron rod to a high 
tower. Before he could carry his proposal into effect, 
Dalibard,at Marly-la-ville,near Paris, taking up FrankHri's 
hint, erected an iron rod 40 feet high, by which, in 17.52, 
he succeeded in drawing sparks from a passing cloud. 
Franklin shortly after succeeded in another way. He 
sent up a kite during the passing of a storm, and found 
the wetted string to conduct electricity to the earth, and 
to yield abundance of sparks. These he drew from a 
key tied to the string, a silk ribbon being interposed 
between his hand and the key for safety. Leyden Jars 
could be charged, and all other electrical effects pro- 
duced, by the sparks furnished from the clouds. The 
proof of the identity was complete. The kite experi- 
ment was repeated by Romas, who drew from a metallic 

1 Franklin enumerates specifically an agreement between electricity and 
lightning in the following respects :— Giving light ; colour of the light ; 
crooked direction ; swift motion ; being conducted by metals ; noise in 
exploding ; conductivity in water and ice ; rending imperfect conductors ; 
destroying animals ; melting metals ; firing inflammable substances ; sul- 
phureous smell (due to ozone y as we now know) ; and he had previously found 
that needles could be magnetised both by lightning andijy the electric spark. 
He also drew attention to the similarity between the pale-blue flame seen 
during thundery weather playing at the tips of the masts of ships (called by 
sailors St. Elmo's FlreX and the "glow" discharge at points. 



CHAP. IV.] ELECTRICITY AND MAGNETISM. ^S 

string sparks 9 feet long, and by Cavallo, who made 
many important observations on atmospheric electricity. 
In 1753 Richmann, of St. Petersburg, who was experi* 
menting with an apparatus resembling that of Dalibard, 
was struck by a sudden discharge and killed. 

303. Theory of Thunderstorms. — Solids and 
liquids cannot be charged throughout their substance ; 
if charged at all the electricity is upon their surface (see 
Art. 29). But gases and vapours, being composed of 
myriads of separate particles, can receive a bodily charge. 
The air in a room in which an electric machine is 
worked is found afterwards to be charged. The clouds 
are usually charged more or less with electricity, derived, 
probably, from evaporation ^ going on at the earth's 
surface. The minute particles of water floating in the 
air being better conductors than the air itself become 
more highly charged. As they fall by gravitation and 
unite together, the strength of their charges increases. 
Suppose eight small drops to join into one. That one 
will have eight times the quantity of electricity dis- 
tributed over the surface of a single sphere of twice the 
radius (and, therefore, of twice the capacity, by Art. 247) 
of the original drops ; and its electrical potential will 
therefore be four times as great. Now a mass of cloud 
may consist of such charged spheroids, and its potential 
may gradually rise, therefore, by the coalescence of the 
drops, and the electrification at the lower surface of the 
cloud will become greater and greater, the surface of the 
earth beneath acting as a condensing plate and becom- 
ing inductively charged with the opposite kind of elec- 
trification. Presently the difference of potential becomes 
so great that the intervening strata of air give way under 
the strain, and a disruptive discharge takes place at the 
point where the air offers least resistance. This light- 
ning spark, which may be more than a mile in length, 
disckarges only the electricity that has been accumulat- 

* Sec Art. 63. 



2S6 ELEMENTARY LESSONS ON fcHAP. iV. 

ing at the surface of the cloud, and the other parts of 
the cloud will now react upon the discharged portion, 
producing internal attractions and internal discharges. 
The internal actions thus set up will account for the 
usual appearance of a thundercloud, that it is a well- 
defined fiat-bottomed mass of cloud which appears at the 
top to be boiling or heaving up with continual move- 
ments. 

304. Lightning and Thunder. — Three kinds of 
lightning have been distinguished by Arago : (i.) The 
Zig-zag flash or *' Forked lightning^^'^ of ordinary occur- 
rence. The zig-zag form is probably due either to the 
presence of solid particles in the air or to local electrifi- 
cation at certain points, making the crooked path' the 
one of least resistance, (ii.) Sheet lightnmg^ in which 
whole surfaces are lit up at once, is probably only the 
reflection on the clouds of a flash taking place at some 
other part of the sky. It is often seen on the horizon at 
night, reflected from a storm too far away to produce 
audible thunder, and is then known as " summer light- 
ning." (iii.) Globular lightnijig^ in the form of balls of 
fire^ which move slowly along and then burst with a 
sudden explosion. This form is very raie, but must be 
admitted as a real phenomenon, though some of the 
accounts of it are greatly exaggerated. Similar phe- 
nomena on a small scale have been produced (though 
usually accidentally) with electrical apparatus. Cavallo 
gives an account of a fireball slowly creeping up the 
brass wire of a large highly charged Leyden jar, and 
then exploding as it descended ; and Plantd has recently 
observed similar but smaller globular discharges from 
his **rheostatic machine" charged by powerful second- 
ary batteries. 

The sound of the thunder may vary with the con- 
ditions of the lightning spark. The spark heats the air 
in its path, causing sudden expansion and compression 
all round, followed by as sudden a rush of air into the 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 25? 

r 

partial vacuum thus produced. If the spark be straight 
and short, the observer will hear but one short sharp clap. 
If its path be a long one and not straight, he will hear 
the successive sounds one after the other, with a charac- 
teristic rattle^ and the echoes from other clouds will 
come rolling in long afterwards. The lightning -flash 
itself never lasts more than Tinjinnr of a second. 

The damage done by a lightning-flash when it strikes 
an imperfect conductor appears sometimes as a disrup- 
tive mechanical' disintegration, as when the masonry 
of a chimney-stack or church-spire is overthrown, and 
sometimes as an effect of heat, as when bell-wires and 
objects of metal in the path of the lightning-current are 
fused. The physiological effects of sudden discharges 
are discussed in Art. -226. The remedy against disaster 
by lightning is to provide an efficient conductor com- 
municating with a conducting stratum in the earth. 

The " return-stroke " experienced by persons in the 
neighbourhood of a flash is explained in Art. 26. 

305. Lightning Conductors. — The first suggest- 
ion to protect property from destruction by lightning 
was made by Franklin in 1749, in the following words : 

" May not the knowledge of this power of points be of use 
to mankind, in preserving houses, churches, ships, etc., from 
the stroke of lightning, by directing us to ^:^ on the highest 
parts of those edifices upright rods of iron made sharp as a 
needle, and gilt to prevent rusting, and from the foot of those 
rods a wire down the outside of the building into the ground, 
or round one of the shrouds of a ship, and down her side till 
it reaches the water ? Would not these pointed rods probably 
;draw the electrical fire silently out of a cloud before it came 
nigh enough to strike, and thereby secure us from that most 
sudden and terrible mischief." 

The four essential points of a good lightning-conductor 
are — (i) that its apex be a fine point elevated above the 
highest point of the building ; (2) that its lower end passes 
either into a stream or into wet stratum of ground ; (3) 

S 



258 ELEMENTARY LESSONS ON [chaI*. IV. 

that the conductor between the apex and the ground be 
perfectly continuous and of sufficient conducting power ; 
(4) that the leads and any iron work or metal work about 
the roofs or chimneys be connected by stout wires with 
the main <:onductor. Too great importance cannot be 
attached to the second and third of theiJe essentials. 
Maxwell has proposed to cover houses with a network 
of conducting wires, without any main conductor, the 
idea being that then the interior of the building will, 
like Faraday's hollow cube (Art. 31), be completely pro- 
tected from electric force. Much controversy has arisen 
of late respecting lightning-rods. Professor Oliver Lodge 
maintaining that a lightning flash to be of the nature of 
an electric oscillation (Art. 295) rather than a current. 
If so, the conductor of least resistance is not necessarily 
the best lightning-rod. Professor Lodge and the author 
independently, and for different reasons, recommend iron 
in preference to copper for lightning-rods. 

306. Atmospheric Electricity. — In 1752 Le- 
monnier observed that the atmosphere usually was in 
an electrical condition. Xavallo, Beccaria, Ceca, and 
others, added to our knowledge of the subject, and 
more recently Quetelet and Sir W. Thomson have 
generalised from more careful observations. The main 
result is that the air above the surface of the earth is 
usually, during fine weather, positively electrified, or at 
least that it is positive with respect to the earth's 
surface, the earth's surface being relatively negative. 
The so-called measurements of " atmospheric electricity " 
are really measurements of difference of potential between 
a point of the earth's surface, and a point somewhere in 
the air above it. In the upper regions of the atmosphere 
the air is highly rarefied, and conducts electricity as do 
the rarefied gases in Geissler's tubes (Art. 292). The 
lower air is, when dry, a non-conductor. The upper 
stratum is believed to be charged with -f- electricity, 
^hile the earth's surface is itself negatively charged 5 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 25$ 

the stratum of denser air between acting like the 
glass of a Leyden jar in keeping the opposite charges 
separate. If we could measure the electric potential at 
different points within the thickness of the glass of a 
Leydeh jar, we should find that the values of the 
potential changed in regular order from a 4- value at 
one side to a — value at the other, there being a point 
of zero potential about half way between the two. Now, 
the air in fine weather always gives + indications, and 
the potential of it is higher the higher we go to 
measure it. Cavallo found more electricity in the air 
just outside the cupola of St. Paul's CatTiedral than 
at a lower point of the building. Sir W. Thomson 
found the potential in the island of Arran to increase 
from 23 to 46 volts for a rise of one foot in level ; but 
the difference of potential was sometimes eight or ten 
times as much for the same difference of level, and 
changed rapidly, as the east wind blew masses of doud 
charged with + or — electricity across the sky. Joule 
and Thomson, at Aberdeen, found the rise of potential 
to be equal to 40 volts per foot, or i -3 volts per centi- 
metre rise of level 

During fine weather a negative electrification of the 
air is extremely rare. Beccaria only observed it six 
times in fifteen years, and then with accompanying 
winds. But in broken weather and during rain it is 
more often — than +, and exhibits great fluctuations, 
changing from — to + , and back, several times in half 
an hour. A definite change in the electrical conditions 
usually accompanies a change of weather. " If, v/hen 
the rain has ceased (said Ceca), a strong excessive ( + ) 
electricity obtains, it is a sign that the weather will 
continue fair for several days." 

307. Methods of Observation. — The older 
observers were content to affix to an electroscope (with 
gold leaves or pith -balls) an insulated pointed rod 
stretching out into the air above the ground, or to fly a 



alto ELEMENTARY LESSONS ON [chap, iv 

kite, or (as Becqiierel did) to shoot into the air an arrow 
communicating with an electroscope by a fine wire, which 
was removed before it fell. Gay Lussac and Biot lowered 
a wire from a balloon, and found a difference of potential 
between the upper arid lower strata of the air. None 
of these methods is quite satisfactory, for they do not 
indicate the potential at any one point. To bring the 
tip of a rod to the same potential as the surrounding air, 
it is necessary that material particles should be discharged 
from that point for a short time, each particle as it 
breaks away carrying with it a + or a — charge until 
the potentials are equalised between the rod and the 
air at that point. Volta did this by means of a small 
flame at the end of an exploring rod. Sir W. Thomson 
has employed a ^\ water- dropper," an insulated cistern 
provided with a nozzle protruding into the air, from 
which drops issue to equalise the potentials : in^ winter 
he uses a small roll of smouldering touch-paper. Dell- 
mann adopted another method, exposing a sphere to 
induction by the air, and then insulating it, and bringing 
it within doors to examine its charge. Peltier adopted 
the kindred expedient of placing, on or near the ground, 
an electrometer of the form shown in Fig. iii, which 
during exposure was connected to the ground, then 
insulated, then removed in-doors for examination. This 
process really amounted to charging the electrometer 
by induction with electricity of opposite sign to* that of 
the air. . The principle of this particular electrometer 
was explained in Art. 260. Of recent years the more 
exact electrometers of Sir W. Thomson, particularly the 
" quadrant " electrometer, described in Art. 262, the 
" divided-ring " electrometer, and a " portable " electro- 
meter on the same general principle, have been used 
for observations on atmospheric electricity. These 
electrometers have the double advantage of giving 
quantitative readings, and of being readily adapted to 
automatic registration, by recording photographically the 



CHAP. IV,] ELECTRICITY AND MAGNETISM. 



261 



movements of a spot of light reflected from a small 
mirror attached to their needle. Using a water-dropping 
collector and a Thomson electrometer, Everett made 




-'^et: 



Fig. III. 



a series of observations in Nova Scotia, and found the 
highest -^ electrification in frosty weather, with a dry 
wind charged with particles of ice. 

308. Diurnal Variations. — Quetelet found that at 
Brussels the daily indications (during fine weather) 
showed two maxima occurring in summer at 8 a.m. and 
9p.m.^ and in winter at 10 a.m. and 6/.^. respectively, 



262 ELEMENTARY LESSONS ON {chap. tv. 

and two mmima which in summer were at the hours o! 
Zp^m. and about midnight. He also found that in January 
the electricity was about thirteen times as strong as in 
June. Observations made by Prof. B. Stewart at Kew 
show a maximum at 8 a.m. in summer at lo a.m. in 
winter, and a second minimum at lo p.m. in summer 
and 7 p.m. in winter. The maxima correspond fairly 
with hours of changing temperature, the minipta with 
those of constant temperature. In Paris, M. Mascart 
finds but one maximum just before midnight : at sun- 
rise the electricity diminishes until about 3 p.m., when it 
has reached a minimum, whence it rises till nightfall. 

Our knowledge of this important subject is still very 
imperfect. We do not even know whether all the 
changes of the earth's electrification relatively to the air 
are due to causes operating above or below the earth's 
surface. Simultaneous observations at different places 
and at different levels are greatly wanted. 

309, The AxiroiU. — In all the northern regions of 
the earth the Aurora borealisy or " Northern Lights," is 
an occasional phenomenon ; and within and near the 
Arctic circle is of almost nightly occurrence. Similar 
lights are seen in the south polar regions of the earth, 
and are denominated. Aurora australis. .As seen in 
European latitudes, the usual form assumed by the 
aurora is that of a number of ill -defined streaks or 
streamers of a pale tint (sometimes tinged with red and 
other colours), either radiating in a fan -like form from 
the horizon in the direction of the (magnetic) north, or 
forming a sort of arch across that region of the sky, of 
the general form shown in Fig. 1 1 2. A certain flicker- 
ing or streaming motion is often discernible in the 
streaks. Under very favourable circumstances the 
aurora extends over the entire sky. The appearance of 
an aurora is usually accompanied by a magnetic storm 
(Art, 145), affecting the compass -needles over whole 
regions of the globe. This fact ^ and the position of the 



CHAP. IV.] ELECTRICITY AND MAGNETISM. 



263 



auroral arches ' and streamers with respect "to the 
magnetic meridian, directly suggest an electric origin 
for the light,— a conjecture which is confirmed by the 
niany analogies found between auroral phenomena and 




.Fig. 112 



those of discharge in rarefied air (Arts. 292 and 294). 
Yet the presence of an aurora does not, at least in our 
latitudes, affect the electrical conditions of the lower 
regions of the atmosphere. On September i, 1859, a 
severe magnetic storm occurred, and aurora were 
observed almost all >over the globe ; at the same time 
a remarkable outburst of energy took place in the 
photosphere of the sun ; but tio simultaneous develop- 
ment of atmospheric electricity was recorded. ^ Aurbrse 
appear in gi-eater frequency in periods of about 11^ 



264 ELEMENTARY LESSONS ON [chap. iv. 

years, which agrees pretty well with the cycles of 
maximum of magnetic storms (see Art. 144) and of 
sun-spots. 

The spectroscope shows the auroral light to be due 
to gaseous matter, its spectrum consisting of a few 
bright lines not referable with certainty to any known 
terrestrial substance, but having a general resemblance 
to those seen in the spectrum of the electric discharge 
through rarefied dry air. 

The most probable theory of the aurora is that origin- 
ally due to Franklin, namely, that it is due to electric 
discharges in the upper air, in consequence of the differ- 
ing electrical conditions between the cold air of the polar 
regions and the \\armer streams of air and vapour raised 
from the level of the ocean in tropical regions by the 
heat of the sun. For evaporation of water containing 
saline matter is a source of electrification (see Art 63), 
the escaping vapour becoming positively electrified. 

According to Nordenskiold the terrestrial globe i? 
perpetually surrounded at the poles with a ring or crown 
of light, single or double, to which he gives the name of 
the *' aurora-glory.*' The outer edge of this ring he esti- 
mates to be at 120 miles above the earth's surface, and 
its diameter about 1250 miles. The centre of the aurora- 
glory is not quite at the magnetic pole, being in lat. 
81® N., long. 80® E. This aurora-glory usually appears 
as a pale arc of light across the sky, and is destitute of 
the radiating streaks shown in Fig. 112, except during 
magnetic and auroral storms. 

An artificial aurora has been produced by Lemstrom, 
who erected on a mountain in Lapland a network of 
wires pres^enting many points to the sky. By insulating 
this apparatus and connecting it by a telegraph v/ire 
with a galvanometer at the bottom of the mountain, he 
was able to observe actual currents of electricity when 
the auroral beam rose above the mountain 



CHAP V ] ELECTRICITY AND MAGNETISM. 265 



CHAPTER V. 

ELECTROMAGNETICS. 

Lesson XXV. — Theory of Magnetic Potential. 

810, That branch of the science of electricity which 
treats of the relation between electric currents and mag- 
netism is termed Blectromagnetics. In Art* 1 1 7 the 
law of inverse squares as applied to magnets was explained, 
and the definition of ** unit magnetic pole" was given in 
Art 125. The student also learned to express the strength 
of poles of magnets in terms of the unit pole, and to apply 
the law to the measurement of magnetic forces. It is, 
however, much more convenient, for the purpose of study, 
to express the interaction of magnetic and electromagnetic 
systems in terms not of '* force" but oi ,^^ potential ^^\ 
i.e. in terms of their power to do work. In Art. 237 
the student was shown how the electric potential due 
to a quantity of electricity may be evaluated in terms of 
the work done in bringing up as a test charge a unit of 
-f electricity from an infinite distance. Magnetic 
potential can be measured similarly by the ideal pro- 
cess of bringing up a unit magnetic pole (N.- seeking) 
from an infinite distance^ and ascertaining the amount 
of work done in the operation. Hence a large number 
of the points proved in Lesson XX. concerning electric 
potential will also, hold true for magnetic potential. The 
student may compare the following propositions with the 
corresponding ones in Articles 237 to 243 ; — 



266 ELEMENTARY LESSONS ON [chap. v. 

(a) The magpie tic potential at any point is the work 
that 7nust be spent upon a unit mag7tetic (N.-seek» 
ing) pole in bringing it ni) to that point from an 
in/inite distance. 

(b) The magnetic potential at any point due to a 
systetn of magnetic poles is the swn of the separate 
magnetic potentials due to the separate poles. 

The student must here remember that the potentials due 
to S. -seeking poles will be of opposite sign to- those due 
to N. -seeking poles, and must be reckoned as negative. 

(c) The {inagnefic) potential at any point due to a 
system of magnetic poles may be calculated (com- 
pare with Art. 238) by sunwiing up the strengths 
of the separate poles divided each by its own 
distance from that point. Thus, if poles of 
strengths ;;/, ni\ m"\ etc., be respectively at 

distances of /, /', /", (x:entimetres) 

from a point P, then the following equation gives 
the potential at P : — 



or \ p = 2 - 
r. 

(d) The difference of {magnetic) potential between 
two points is the work to be done on ^r by a 
unit {N.- seeking) pole in moving it from one 
poifit to the other. 

(e) Magnetic force is the rate of change of {magnetic) 
potejttial per unit of length. 

(f) Equipotential stirfaces are those {imaginary) sur- 
faces surrounding a 7nagnetic pole or system oj 
poles, ovef which the {magnetic) potential has 
equal values. Thus, around a single magnetic 
pole, supposing all the magnetism to be collected 
at a point far removed from all other poles, the 
potential would be equal all round at equal 



CHAP. V.J ELECTRICITY AND MAGNETISM. 267 

distances ; and the equipotential surfaces would 
be a system of concentric spheres at such dis- 
tances apart that it would require the expendi- 
ture of one erg of work to move a unit pole up 
from a point on the surface of one sphere to any 
point on the next (see Fig. 97). Around any real 
magnet possessing two polar regions the equi- 
potential surfaces would be much more com- 
plicated. Magnetic force^ whether of attraction 
or repulsion^ always acts across the equipotential 
surfaces in a direction 7iormal to the surface ; the 
magnetic lines of force are everywhere perpen- 
dicular to the equipotential surfaces. 

311. Tubes of Force. — The following proposi- 
tion is also important : — From a single magnetic pole 
(supposed to be a point far removed from all other 
poles) the lines of force diverge radially in all directions. 
The space around may be conceived as thus divided up 
into a number of conical regions, each having their apex 
at that pole ; and througii each cone, as through a tube, a 
certain number of lines of force will pass. Such a conical 
space may be called a "tube of force." No matter 
where you cut across a tube of force the cross-section 
will cut through all the enclosed lines of force, though 
they diverge more widely as the tube widens. Hence, 
(g) The total inagnetic force exerted across any section 

of a tube of force is constant wherever the section 

be taken. 

In case the magnetism is not concentrated at one 
point, but distributed over a surface, we shall have to 
speak of the " amount of magnetism " rather than of the 
•* strength of pole," and in such a case the 

(h) JMagnetic density is the amount of free magnetism 
per unit of surface. In the case of a simple 
magnetic shell over the face of which the 
magnetism is distributed with uniform density, 



268 ELEMENTARY LESSONS ON [chap. v. 

the ^'strength" of the shell will be equal to the thick- 
ness of the shell multiplied by the surface-density. 

' 312. Intensity of Field. — We have seen (Art. 105) 
that every magnet is surrounded by a certain '' field," 
v/itliin which magnetic force is observable. We may 
completely specify the properties of the field at any 
point by measuring the stre?tgth and the dtrectton of 
that force, — that is, by measuring the '* intensity of 
the yield ^^ and the direction of the lines of force. The 
^^ intensity of the field ^^ at any foint is 7neasured by the 
force with which if acts on a unit magnetic pole placed 
at that point. Hence, unit intensity of field is that 
intensity of field which acts on a unit pole with a force 
of one dyne. There is therefore a field of unit intensity 
at a point one centimetre distant from the pole of a 
magnet of unit strength. Suppose a magnet pole, whose 
strength is m^ placed in a field at a point where the 
intensity is H, then the force will be m times as great 
as if the pole were of unit strength, and 

f ^ m X H. 

We may also take as a measure of the intensity of 
the field at any point the number of lines of force that 
pass through a square centimetre of surface placed 
across the field at that point. // follows that a unit 
magnetic pole will have 47r lines of force proceeding from 
it : for there is unit field at unit distance away, or one 
line of force per square centimetre ; and there are 47r 
square centimetres of surface on a sphere of unit radius 
drawn round the pole. A magnet, whose pole-strength 
is 7n^ has ti^irm lines of force running through the steel, 
and diverging at its pole. 

313. Intensity of Magnetisation : Magnetic 
Susceptibility and Magnetic Permeability. — 
When a piece of magnetic metal is placed in a magnetic 



CHAP, v.] ELECTRICITY AND MAGNETISM. 269 

field, some of the lines of magnetic force run through it 
and magnetise it. The intensity of its magnetisation 
will depend upon the intensity of the field into which it 
is put and upon the metal itself. There are two ways 
of looking at the matter, each of which has its advant- 
ages. We niay think of the magnetism of the iron or 
other metal as something resident on the polar surfaces, 
and expressed therefore in units of magnetism : or we 
may think about the internal condition of the piece of 
metal, and of the number of magnetic lines that are 
running through it and emerging from it into the sur- 
rounding space. This is the more modern way. The 
fact that soft iron placed in the magnetic field becomes 
highly magnetic may then be expressed in the following 
two ways : — (i) iron when placed in the magnetic field 
develops strong poles on its end surfaces, being highly 
susceptible to magnetisation ; (2) when iron is placed in 
the magnetic field, the magnetic lines gather themselves 
up and run in greater quantities through the space 
now occupied by iron, for iron is very permeable to the 
lines of magnetic induction, being a good conductor of 
the magnetic lines. Each of these ideas may be 
rendered exact by the introduction of appropriate 
coefiicients. 

The coefl&cient of magnetisation, or Buscepti- 
bility, is based on unit of pole strength. Suppose a 
magnet to have m units of magnetism on each pole ; 
then if the length between its poles is /, the product 
m y. I \% called its magnetic moment^ and the magnetic 
moment divided by its volume is called its ifiiensity of 
magnetisation ; this term being intended, though based 
on surface-unit of pole strength, to convey an idea as to 
the internal magnetic state. Seeing that volume is the 
product of /sectional area into length, it follows that if 
any piece 01 iron or steel of uniform section had its 
surface magnetism situated on its ends only, its intensity 
of magnetisation would be equal to the strength of pole 



270 ELEMENTARY LESSONS ON [chap. v. 

divided by the atea of end surface. Writing I for tbe 
intensity of magnetisation we should have 

T mag, moment vt X I m 

volume s X I s ' 

Now, supposing this intensity of magnetisation • were 
due to the iron having been put into a magnetic field of 
intensity H, we find that the ratio between the resulting 
intensity of magnetisation I and the magnetising force 
H producing it is expressible by a numerical coefficient 
of magnetisation, or susceptibility^ k. We may write : 

I =>&H 
or >&==i 

This may be looked at as saying that for every mag- 
netic line in the field there will be k units of magnet- 
ism on the end surface. 

In magnetic substances such as iron, steel, nickel, 
etc., the susceptibility k has positive values ; but there 
are many substances such as bismuth, copper, mercury, 
etc., which possess feeble negative coefficients. These 
latter are termed " diamagnetic " bodies (Art.. 339) ^i^d 
are repelled by the poles of magnets. The values of k 
vary very much* in iron, not only in the different qualities 
of iron, but vary in every specimen with the stage of 
magnetisation. , When a piece of iron has become well 
magnetised it is no longer as susceptible to magnetisa- 
tion as it was at first : it is becoming ^^ saturated.'* 
Barlow found the value oi k for iron to be 32-8, Thalen 
found it from 32 to 44, Archibald Smith 80 to 90, 
Stoletow 21 to 174 ; Rowland found Norwegian iron to 
go as high as 366 ; Ewing found thin soft Tron wires go 
up to 1300 or 1400. Stoletow showed that iron in a 
weak magnetic field showed a small susceptibility, which 
greatly increased as the magnetising force in the field 
was strengthened, but again fell off with still greater 
forces as the iron got saturated. When very intense 



eHAF. v.] ELECTRICITY AND MAGNETISM. 271 

magnetising forces are used, so that the intensity of 
magnetisation is very great, the susceptibility (and per- 
meability) is practically reduced to zero. It appears 
that the maximum intensity of magnetisation that can 
be given to kon and steel is about 1500 (units, per 
square centimetre of cross section). According to 
Rowland the maximum for cobalt is 800, for nickel 
494. Steel does not retain all the magnetisation that 
can be temporarily induced in it, its maximum intensity 
being, according to Weber 400, according to Von 
Waltenhofen 470, according to Rowland 785, accord- 
ing to Hopkinson 878. Everett has calculated (from 
Gauss's observations) that the intensity of magnetisation 
of the earth is only 0-0790, or only ^y^^^ of what it 
would be if the globe were wholly -iron. In weak mag- 
netic fields the susceptibility of nickel exceeds by about 
five times that of iron ; but in strong fields iron is more 
susceptible. 

The ooeflQoient of magnetic Induction, or per- 
meability, is based on the lines of magnetic induction. 
The number of magnetic lines that run through unit 
area of cross section, at any point, is called ^^ the mag- 
netic induction " at that point : it is denoted by the 
letter B. The ratio between the magnetic induction 
and the magnetising force producing it is expressed by 
a numerical coefficient of induction, or permeability^ fx. 
We therefore write 

B = /i H 
or /^ = |. 

This coefficient is always positive : for empty space it 
IS I, for air it is practically i ; for magnetic materials it 
is greater than i, for diamagnetic materials it is slightly 
less than i. The student may think of it in the follow- 
ing way : Suppose a certain magnetising force to act in 
a certain direction, there would naturally result firom its 
action induction along a certain number of lines of in- 



t^Jl 



ELEMENTARY LESSONS ON [chap. v. 



duction (or so-called lines of force), and in a vacuum 
the number of lines would numerically represent the 
magnetising force. But if the space considered were 
occupied by iron the same magnetising force would 
mduce manx more lines. The iron has a sort of multi- 
plying power or specific inductive capacity, or conduc- 
tivity for the magnetic lines. This permeability is easily 
calculated from the susceptibility. It was shown at end 
of Art. 3 1 2 that there are 47r magnetic lines proceeding 
from each unit of pole magnetism. Hence if, as shown 
above, each line of force of the magnetising field pro- 
duces k' units of magnetism there will be ^irk lines 
added by the iron to each i line in the field, or the 
multiplying power of the iron {x is equal to i + 47rk. 
The values of the permeability, like those of suscepti- 
bility, decrease as the magnetisation of the iron gets in- 
creased towards saturation. In the following Table two 
sets of values are given from the researches of Stole- 
tow, and the more recent ones of Bidwell. 



H 


A 


I 


M 


B 




Observations of 


• Stoletow 




043 


21-5 


924 


275-6 


118-5 


044 


305 


»3-4S 


3905 


171 8 


3-20 


1740 


556-6 


2222 


7tJ3 


30-6 


39 4 


i2o6- 


504 -2 


15427- 




Observations 


F Bidwell. 




3 9 


151-0 


587 


1899-1 


7390 


103 


891 


918 


1121*4 


»»55o 


40- . 


J07 


1226 


3864 


1546a 


"5 


II-9 


1370 


1507 


17330 


208- 


7-0 


145^ 


88-8 


18470 


.427- 


35 


1504 


45-3 


>9330 


585- 


2-6 


1530 


33 9 


19820 



CHAP, v.] ELECTRICITY AND MAGNETISM. 273 



According to Hopkinson the induction B for cast 
iron is about 1 1,000, in a field H of 220 : the residual 
induction being about 5000. Bosanquet finds maxi- 
mum induction B for charcoal iron and wrought iron 
from 16,800 to about 19,000; but has succeeded in 
magnetising a wrought iron bar so that the induction in 
the middle bit of the bar reached 29,388. Steel con- 
taining 1 2 per cent of manganese is curiously non-mag- 
netic. Hopkinson found its maximum induction only 310. 

314. Potential due to a (Solenoidal) Magnet. 
— A long thin uniformly magnetised magnet exhibits 
free magnetism only at the two ends, and acts on 
external objects just as if there were two equal quantities 
of opposite kinds of magnetism collected at these two 
points. Such a magnet is sometimes called a solenoid 
to distinguish it from a magnetic shell (Art. 107). 
Ordinary straight and horse-shoe shaped magnets are 
imperfect solenoids. The magnetic potential due to a 
solenoid, and all its magnetic effects, depend only on 
the position of its two poles, and on their strength, and 
not on the form of the bar between them, whether straight 
or curved. In Art. 3 10 (^) was given the rule for finding 
the potential due to a system of poles. Suppose the 
two poles of a solenoid have strengths + m and — fn 
(taking S. -seeking pole as of negative value), and that 
the respective distances of these poles from an external 
point P, are r^ and r^ : then the potential at P will be, 

Suppose a magnet curled round until its N. and S. 
poles touch one another : it will not act as a magnet 
on an external object, and will have no " field " (Art. 
105); for if the two poles are in contact, their distances 
r, and r^ to an external point P will be equal, and 

(^ ^) will be = 

315. 'Potential due to a Magnetic Shell. — 
Gauss demonstrated that the_ i)otential due to a magnetic 



2^4 ELEMENTARY LESSONS ON [chap. v. 

shell at a point near it is equal to the strength of the 
shell multiplied by the solid-angle subtended by the shell 
at that point J the ^* strength " of a magnetic shell 
being the product of its thickness into its surface-density 
of magnetisation. 

If CO Represents tne solid-angie subtended at the pomt 
P, and / the strength of the shell, then . 

Vp = (0 /. 

Proof, — To establish this proposition would require an easy 
application of the integral calculus. But the following geo- 
metrical demonstration, though incomplete, must here suffice. 

Let us consider the shell as comoosed, like that drawn, of 
^ series of small elements of 

thickness /, and having each an jf^ 

area of surface s. The whole /^ \\\ 

solid -angle subtended at P by ^^.--'''"^ — "^X^n iXv"*-^ 

the shell may liKcwise be con- /^ -y"^^^^/ *""t'"^-\ 

ceived as made up of a number \s^ /^v/ \^^ 

of elementary small cones, each \J"^""~-~C=^Z ^--^^^^^''^ y 

of solid -angle c6 : Let r^ and r^ ^^--^.^.JCL^ \^,^^^^-^ 

be the distances from P to the p. 

two faces of the element : Let 

a section be made across the small cone ortnogonally, or at 

right angles to r^, and call the ,area of this section a : Let the 

angle between the surfaces s and a be called angle p : then 

s = -^. Let i be the ^^ strength" of the shell [i.e. = its 
cos j8 ^ 

surface-density of magnetisation x its thicksiess) ; then --- = 

surface-density of magnetisation, and ^ -^ = strength of either 

pole of the little magnet == m, 

,.j , , area of us orthogonal section 
Now solid angle c& = -3-^ ^ 

a\ 

= 1^ '. 

therefore ^ = c6^, 

(br^ 
and s = 



cos ^ 



c/IXl. v.] FXECTRICITY AND MAGNETISM. 275 



But the potential at P of the magnet whose pole is w, will be 

Cf a m ( ) 



=s CiZ 






but - - 1= -^ -TL^ which we may write — i— --3 

because r^ and r^ may be made as nearly equal as we please. 
And since r^ -- t\ ^ t cos j3 

r^ / / cos /3 \ 



7' = (&i 



if cos /? 
e» = ^i 

or the potential due to the element of the shell = the. strength 
of the shell x the solid-angle subtended by the element' of the 
shell. Hence, if V be the sum of all the values of v^ fot all the 
different elements, and if w be the whole solid -angle (tlie sum 
of all the small solid-angles such as cfi), 
Vp = w/ 

or, the potential due to a magnetic shell at a point is equal to 
the strength of the shell multiplied by the solid-angle subtended 
by the whole of tlie shell at that point. 

Hence (oi represents the work that would have to be 
done on or by a unit -pole, to bring it up from an 
infinite distance to the point P, where the shell subtends 
the solid-angle co. At a point Q where the solid-angle 
subtended by the shell is different, the potential wall be 
different, the difference of potential between P and Q 

^i^g Vq ~ Vp = /(cOq - (Op). 

If a magnet-pole whose strength is m were brought 
up to P, m times the work would have to be done, or 
the mutual potential would be = moiz. 

316. Potential of a Magnet-pole on a ShelL — 
It is evident that if the shell of strength / is to be 
placed where it subtends a solid-angle oj at the pole ^, 
it would require the expenditure of the same amount of 
work to bring up the shell from an. infinite distance 
on the one hand, as to bring up the magnet-pole :roru 



276 ELEMENTARY LESSONS ON [chap. v. 

an infinite distance on the other ; hence m<Aii represents 
both the potential of the pole on the shell and the 
potential of the shell on the pole. Now the lines of 
force from a pole may be regarded .as proportional in 
number to the strength of the pole, and from a single 
pole they would ra^diate out in all direptions equally. 
Therefore, if a magnet-pole was placed at P, at the apex 
of the solid-angle ,of a cone, the number of lines of force 
which would pass through the solid-angle would be pro- 
portional to that solid-angle. It is therefore convenient 
to regard /^/co as representing the number of lines of force 
of the pole which pass through the shell, and we may call 
the number so intercepted N. Hence the potential of a 
magnet-pole on a magnetic shell is equal to the strength 
of the shell multiplied by the number of lines of force 
{due to the magnet-pole^ which pass through the shell j 
or V = N/. If either the shell or the pole were moved 
to a point where a different number of lines of force 
were cut, then the difference of potential would be, 

V<, - Vp = +/ (N^ - Np). 

This formula is of great importance : but the student 
must be specially cautioned as to the signs to be 
attributed in applying it to the various quantities. A 
magnet has two poles (N.-seeking and S.-seeking), whose 
strengths are + m and — m^ and the two faces of a 
magnetic shell are of opposite sign. To bring up a N.. 
seeking (or +) pole against the repelling force of the 
N.-seeking face of a magnetic shell requires a positive 
amount of work to be done ; and their mutual reaction 
would enable work to be done afterwards by virtue of 
their position : in this case then the potential is -F. But 
in moving a N.-seeking pole up to the S.-seeking face of 
a shell work will be done by the pole, for it is attracted 
up ; and as work done by the pole may be regarded as 
our doing negative work, the potential here will have a 
negative value. 



CHAP, v.] ELECTRICITY AND MAGNETISM. 2^7 

Again, suppose -we could bring up a unit N.-seeking 
pole against the repulsion of the N.-seeking face of a 
shell of strength /, and should push it right up to the 
shell ; when it actually reached the plane of the shell the 
shell would occupy a whole horizon, or half the whole 
space ar<mnd the pole, the solid-angle it subtended being 
therefore 2-^,^ and the potential will be + 2^/. If we 
had begun at the S.-seeking face, the potential at that 
face would be — 2rf. It appears then that the potential 
alters its value by ^m on passing from one side of the 
shell to the other. 

317. Reaction between a Pole and a Magnetic 
Shell. — Again, Figs. 52 and 53 will show graphically 
that lines of force from two poles of opposite kind run 
into one another, whilst those from similar poles turn 
aside as if mutually repellant. If a N.-seeking pole be 
brought up to the N.-seeking face of a shell few or none 
of the lines of force of the magnet will cut the* shell ; 
whereas if a N.-seeking pole be brought up to the 
S.-seeking face of a shell, large numbers of the lines will 
be cut by the shell and the pole, as a matter of fact, will 
be attracted up to the shell, where as many lines of force 
as possible are cut by the shell. We may formulate this 
action by saying that a magnetic shell and a mag7iet-pole 
react on one another and urge one another in such a 
direciio7i as to make the number of lines of force that are 
cut by the shell a maxi7nu77U (T^Iaxwell's Rule, Art. 193). 
Outside the attracting face of the shell the potential is — w/, 
and the pole moves so as to make this negative quantity 
as great as possible, or to make the potential a minimum. 
Which is but another way of putting the matter as a 
particular case of the general proposition that bodies 
tend to move so that the energ)^ tliey possess in virtue 
of their position tends to run down to a minimum. 

318. Magnetic Potential due to Current. — The 
propositions concerning magnetic shells given in JtVie 

I Sec note on Ways of Reckoning Angles, Art 133^ 



278 ELEMENTARY LESSONS ON [chap. v. 

preceding paragraphs derive their great importance 
because of the fact laid down in Art 192 that circuits, 
traversed by currents of electricity, behave like magnetic 
shells. And for the purpose of calculating the magnetic 
effects due to currents by applying these theorems, it is 
necessary to adopt the electromagnetic unit of the 
strength of current explained in Art. 196. If we adopt 
such a unit we may at once go back to Art. 315, and 
take the theorems about magnetic shells as being also 
true of closed voltaic circuits. 

(a,) Potential duo to closed circuit (compare 
Alt. 315). 

T/ie potential V due to a closed voltaic circint (traversed 
by a current) at a point P near it^ is equal to the strength 
of the current multiplied by the solid- angle o) subtended 
by the circzdt at that point. If / be the strength of the 
current in electromagnetic units, then 

Vp = - (fii. 

The reason for adopting the negative sign is the following : — 
The potential (/.<?. the work done on a unit N, -seeking 
pole) is reckoned positive where the work is done 
against repulsion Now, if a N. -seeking pole is to be 
brought up to a point opposite the repelling face of a 
circuit, it must (see Fig. 115) be brought up to that face 
round which the electricity is flowing in the counter- 
clock -wise or negative direction, or round which the 
current must be considered as having strength = — L 
The student may be helped to understand this conven- 
tion about signs by remembering (see Fig. 115) that 
when he is looking at the S.-pole of an electromagnet 
he is looking along the magnetic lines of force in their 
positive direction, and that the current is running clock- 
wise round the coil. Or, the positive direction of line3 
of force through the circuit is associated with a (positive) 
rotation round the circuit, as is the forward thrust v/itb 
the right-handed rotation in the operation of driving an 
ordinary right-handed screw. 

{b^ At a point Q, where the solid -angle subtended by 



chaf; v.] electricity AND MAGN'ETISM. 27I 



the circuit is otf^ instead of a;p, the potential will have a 
different value, the difference of potential, being, 

319. (c.) Mutual Potential of a Magnet-pole 
and a Circuit. — If a magnet -pole of strength m were 
brought up to P, where the circuit subtends a solid-angle 
0), from an infinite distance against the magnetic forces 
exercised by the current, m times as much work will be 
done as if the magnet-pole had been of unit strength, and 
the work would be just as great whether the pole m were 
brought up to the circuit, or the circuit up to the pole. 
Hence, the mtitual potential will be 

But, as in Art. 316, we may regard mta as representing 
the number of lines of force of the pole which are 
intercepted by and pass through the circuit, and we 
may write N for that number, and say 

V = - /-N, 

or the mutual potential of a magnet-pole and a circuit 
is equal to the strength of the current multiplied by the 
7ttimber hf the magnet -pole^s lines of force that are inter- 
cepted by the circuity taken with reversed sign. 

(^.) As in the case of the magnetic shell, so with the 
circuit, the value of the potential changes by 4^^/ from a 
point on one side of the circuit to a point just on the 
other side ; that is to say, being — 2m on one side and 
+ 2^/ on the other side, work equal to 4^/ must be 
done in carrying a unit-pole from one side to the other 
round the outside of the circuit. The work done in 
thus threading the circuit along a path looped n times 
round it would be ^n^Tri. 

320. {e) Mutual Potential of two Circuits. — Two 
closed circuits will have a mutual potential, depending on 
the strengths of their respective currents, on ih^x distance 
apart, and on their form and position. If their currents 



28o ELEMENTARY LESSONS ON [chap, v. 



be respectively / and /'. and if the distance between two 
elements ds and ds' of the circuits be called r, and e the 
angle between the elements, it can be shown that their 

mutual potential is = - iiJJ ^^-^ ds ds'. This expressior 

represents the work that would have to be done to 
bring up either of the circuits from an infinite distance 
to its present position near the other, and is a negative 
quantity if they attract one another. Now, suppose the 
strength of current in each circuit to be unity ; their mutual 

potential will iu that case ^^//^^— ^^ ^^\ ^ quantity whicli 

depends purely upon the geometrical form and position 
of the circuits, and for which we may substitute the 
single symbol M, which we will call the ^* coefficient oj 
mutual potential :^^ we may now write the mutual 
potential of the two circuits when the currents are i and 
;" as = - iilsl. 

But we have seen in the case of a single circuit that 
we may represent the potential between a circuit and a 
unit-pole as the product of the strength of the current 
- / into the number N of the magnet-pole's lines of force 
intercepted by the circuit. Hence the symbol M must 
represent the number of each other's lines of force 
mutually intercepted by both circuits, if each carried 
unit current. If we call the two circuits A and B, then, 
when each canies unit current, A intercepts M lines of 
force belonging to B, and B intercepts M lines of force 
belonging to A. 

Now suppose both currents to run in the same 
(clock-wise) direction ; the front or S.-seeking face of one 
circuit will be opposite to the back or N. -seeking face of 
the other circuit, and they will attract one anotherj and 
win actually do work as they approach one another, or 
(as the negative sign shows) negative work will be done 
in bringing up one to the other. When they have 
attracted one another up as much as possible the circuits 
will coincide in^ direction and position as nearly as can 



CHAP, v.] ELECTRICITY AND MAGNETISM. 281 



ever be. Their potential energy will have run down to 
its lowest^ minimum, their mutual potential being a neg- 
ative maximum, and their coefiScient of mutual potential 
M, having its greatest possible value. Two circuits, 
then, are urged so that their coefficient of mutual potential 
M shcdl have the greatest possible value. This justifies 
Maxwell's Rule (Art. 193), because M represents the 
number of lines of force mutually intercepted by both 
circuits. And since in this position each circuit induces 
as many lines of magnetic force as possible through the 
other, the coefficient of mutual potential M is also called 
the coefficient of mutual induction. 

NOTE ON MAGNETIC AND ELECTRO- 
MAGNETIC UNITS. 

821. Magnetic Units. — All magnetic quantities, strength of 
poles, intensity of magnetisation, etc., are expressed in terms of 
special units derived from the fundamental units of lengthy mass, 
and time^ explained in the Noie on Fundamental and Derivea 
Units (Art. 254). Most of the following units have been directly 
explained in the preceding Lesson, or in Lesson XI. | the others 
follow from them. 

Unit Strength of Magiutic Pole. — ^The unit magnetic pole is 
one of such a strength, that when placed at a distance of 
one centimetre (in air) from a similar pole of equal 
strength, repels it with a force of one djme (Art. 125). 
Magnetic Potential. — Magnetic potential being measured by 
work done in moving a unit magnetic pole against the 
•magnetic forces, the unit of magnetic potential will be 
measured by the unit of work, the erg. 
Unit Difference of Magnetic Potential — Unit difference of 
magnetic potential exists between two points when it 
requires the expenditure of one erg of work to bring a 
(N. -seeking) unit magnetic pole from one point to the 
other against the magnetic forces. 
Intensity of Magnetic Field \% measured by \}[iz force it exerts 

upon a unit magnetic pole : hence, 
Unit Intensity of Field is that intensity of field which acts 
Oil a unit (N. -seeking) pole with a force of one dyne. 



282 ELEMENTARY^ LESSONS ON [chap. v. 

322. Electromagnetic Units. — The preceding magnetic 
units give rise to the following set of electrical units, in which 
the strength of currents, etc., aie expressed in magneHc measure. 
The relation of this ** electromagnetic " set of units to the 
** electrostatic'* set of units of Art. 257 is explained in Art. 

365. 

Unii Strength ofCttrrent, — A current ha« unit strength when 

one centimetre length of its circuit bent into an arc c >f 

one centimetre radius (so as to be always one centim. 

away from the magnet-pole) exerts a force of one dyne 

on a unit magnet-pole placed at the centre (Art. 196). 

Unit of Quantity of Electricity is that quantity which is 
conveyed by unit current in one second. 

Unit of Difference of Potential (or of Electromotive force). 
Potential is work done on a unit of electricity ; hence 
unit difference of potential exists between two points 
when it requires the expenditure of one erg of work to 
bring a imit of + electricity from one point to the other 
agaiuit the electric force. 

Unit of Resistance. — A conductor possesses unit resistance 
when unit difference of potential between its ends causes 
a current of unit strength [i.e. one unit of quantity per 
second) to fiow tlirough it. 

323. Practical Units — Several of the above *• absolute" 
units would be inconveniently large and others inconveniently 
small for practical use. The following are therefore chosen 
instead, as electromagnetic imits : — 

Electromotive-foj'ci. — The Volt, = 10^ absolute units (being 
a little less than the E.M.F. of one DanielPs cell). 

Resistance.— 1\iQ Ohm, = 10^ absolute units of resistance 
(and theoretically the resistance represented by the velo- 
city of one earth-quadrant per second). (See Art. 364.) 

Curreiit. — As a practical unit of current, that furnished by a 
potential of one volt through one ohm is taken, being 
10— "^ of an absolute (electro-magnetic) unit of current, 
and is known as one Ampere (formerly one ^^weber"). 

Quantity.— T\iQ Coulomb, = 10— "^ absolute units of quantity 

of the electromagnetic system. 
Capacity. — The Farad, = 10-^ (or one one -thousand - 

millionth) of absolute unit of capacity. 



CHAP, v.] ELECTRICITY AND MAGNETISM. 



283 



Seeing, however, that quantities a million times as great as 
some of these, and a million times as small as some, have to be 
measured by electricians, the prefixes mega- and micro- are 
sometimes used to signify respectively *^ one million " and ** one- 
millionth part." Thus a megohm is a resistance of one million 
ohms, a microfarad a capacity of j^qqq^qoo of a farad, etc 
The prefix milli- is firequently used for ** one-thousandth part ;" 
thus a milli-amp^re is the thousandth part of one ampere. 
' Tfiis system of ** practical " units was devised by a committee 
of the British Association, who also determined the value of the 
**ohm" by experiment, and constructed standard resistance 
coils of german-silver, called **B. A. Units" or **ohms." 
The " practical " system may be regarded as a system of units 
derived not from the fundamental units of ce^itimetre^ gramme^ 
and second^ but from a system in which, while the unit of time 
remains the second, the units of length and mass are respectively 
the earth-quadrant and lo — ^^ gramme. 

324. Dimensions of Magnetic and Electromagnetic Units. 
— The fundamental idea of " dimensions " is explained in Art. 
258. A little consideration will enable the student to deduce 
for himself the following table — 



Units. 



{Magnetic. ) 

Strength of pole 
Quantity of magnetism 

Magnetic Potential 

Intensity of Field 

^^Electro-magnetic.) 
Current (strength) 
Quantity 

Potential ) 

Electromotive- Force \ 
Resistance 
Capacity 



= Vforce X (distance)^ = 

=s work -7- strength of pole = 

= force -T- strength of pole = 

= intensity of field x length = 

= current X time s= 

= work -^ quantity ~ 

=: E.M.F. -r- current = 

= quantity -f- potential = 



Dimensions 



m4 l^T^ 

MiL^T"" 

M^L-^T" 

m4 L^ T"" 

Mi L^T"' 
LT-^ 



2S4 ELEIMENTARY LESSOXS ON [chap. V. 



NOTE ON MEASUREMENT OF EARTH'S MAGNETIC 
FORCE IN ABSOLUTE UNITS. 

325a. The intensity of the earth's magnetic force at any place is 
the force with which a magnet-pole of unit strength is attracteil. 
As explained in Art. 138, it is usual to measure the horizontal 
component H of this force, and from this and the cosine of the 
angle of dip to calculate the total force I, as the direct deter- 
mination of the total force is surrounded with difficulties. To 
determine H in absolute (or C.G.S.) units^ it is necessary to 
make two observations with a magnet of magnetic moment T^I ; 
(the magnetic moment being, as mentioned in Art. 313, the 
product of its length into the strength of one of its poles). In 
one of these observations the product IMH is determined by a 

method of oscillations ; in the second the quotient jj is deter- 
mined by a particular method of deflection. The square root of 
the quantity obtained by dividing the former by the latter will, 
of course, give H. 

(i;) Determination ^MH. — The time / of a complete oscilla- 
tion to-and-fro of a magnetic bar is 

/^ 

t =. 2ir \ HM ' 

where K is the *'aioment of inertia" of the magnet This 
formula is, however, only true for very small arcs of vibration. 
By simple algebra it follows that 

t^ . 

Of these quantities / is ascertained by a direct observation of 
the time of oscillation of the magnet hung by a torsionless fabre : 
and K can be either determined experimentally or by one of the 
following formulas : — 

//2 a- \ 
For a round bar K = «/ 1 — + — I, 

\I2 4 /' 

j . 

where w is the mass of the bar in grammes, / its length, a 



CHAP, v.] ELECTRICITY. AND MAGNETISM. 285 



its radius (if round), b its breadth, measured horizontally (if 

rectangular). 

M 
(ii.) Determination of -jj. — The magnec is next caused to 

deflect a small magnetic needle in the following manner, 
** broadside on." The magnet is laid horizontally at right 
angles to the magnetic meridian, and so that its middle point is 
(magnetically) due south or due north of the small needle, and 
at a distance r from its centre. Lying thus broadside to the 
small needle its N.-pole will repel, and its S.-pole attract, the 
N. -pole of the needle, and will exercise contrary actions on the 
S.-pole of the needle. The total action of the magnet upon the 
needle will be to deflect the latter through an angle 5, whose 

M 
tangent is directly proportional to jj, and inversely propor- 
tional to the cube of the distance r ; or 

-I = r3 tan 5. 

Dividing the former equation by this, and taking the square root, 
we get, 



«=?/ 



K 



r^ tan 5. 



NOTE ON INDEX NOTATION. 

32Sb. Seeing that electricians have to deal with quantities 
requiring in some cases very large numbers, and in other cases 
very small numbers, to express them, a system of index notation 
is adopted, in order to obviate the use of long rows of cyphers. 
In this system the significant figures only of a quantity are put 
down, the cyphers at the end, or (in the case of a long decimal) 
at the beginning, being indicated by an index written above. 
Accordingly, we may write a thousand (=10x10x10) as 
ro^ and the quantity 42,000 may be written 42 x 10^. The 
British National Debt of ;!^77o,ooo,ooo may be written £^^^ x 
lo''. Fractional quantities will have negative indices when 
written as exponents. Thus ^Jir (=0'oi), = 1-4-10-^- 
10 =:^io~2. And so the decimal 0*00028 will be written 
28 X io~^ (being = 28 x '00001). The convenience of this 
method will be seea by an example or two on electricity. 
The electrostatic capacity of the earth is 630,000,000 times 



286 



ELEMENTARY LESSONS ON [chap. v. 



that of a sphere of one centimetre radius, =63 x lo'^ (electro- 
static) units The magnetic moment of the earth is, accoiding 
to Gauss, no less than 85,000,000,000,000,000,000,000,000 
times that of a magnet of unit strength and centim. length, i,e, 
its magnetic moment is 85 x lo^^ units. The resistance of 
selenium is about 40,000,000,000, or 4 x 10^^ times as great as 
that of copper ; that of air is about lo^^, or 

1 00, 000, 000, 000, 000, 000, 000, 000, 000 
times as great. The velocity of light is about 30,000,000,000 
centimetres per second, or 3 x lo^^. As a final example we 
may state that the number of atoms in the universe, as far as 
the nearest fixed star, can be shown to be certainly fewer than 
7 X io»^ 

Lesson XXVL — Electro7)iagnets. 

323. Electromagnets. — In 1820, almost immedi- 
ately after Oerstedt's discovery of the action of the 
electiic current on a magnet needle, Arago and Davy 
independently discovered how to magnetise iron and 
steel by causing currents of electricity to circulate round 
them in spiral coils of wire. The method is shown in the 




Fig. II4* 



simple diagram of Fig. ii4j where a current from a 
single cell is passed through a spiral coil of wire, in the 



CHAP, v.] KLLCTRICITY AND MAGNETISM. 287 

hollow of which is placed a bar of iron or steely, which is 
thereby magnetised. The separate turns of the coil 
must not touch one another or the central bar, other- 
wise the current will take the shortest road open to it 
and will not traverse the whole of the coils. To pre- 
vent such short-circuiting by contact the wire of the coil 
should be overspun with silk or cotton (in the latter case 
insulation is improved by steeping the cotton covering in 
melted paraffin wax) or covered with a layer of gutta- 
percha. If the bar be of iron it will be a magnet only 
so long as the current flows ; and an iron bar thus sur- 
rounded with a coil of wire for the purpose of magnetising 
it by an electric current is called an Electromagnet. 
Sturgeon, who gave this name, applied the discoveries 
of Davy and Arago to the construction of electromagnets 
far more powerful than any magnets previously made. 
It was first shown by Henry that when electromagnets 
are required to work at distant end of a long line they 
must be wound with many turns of fine wire. 

By applying Ampere's Rule (Art. 186), we can find 
which end of an electromagnet will be the N.-seeking 
pole ; for, imagining ourselves to be swimming in the 
current (Fig. 114), and to face towards the centre where 
the iron bar is, the N.-seeking pole will be on the left. 
It is convenient to remember this relation by the fol- 
lowing rules : — Lookmg at the S, -seeking pole of an 
electromagnet^ the magnettsmg currents are circulating 
round it in the same cyclic direction as the hands of a 
clock move J and, looking at 
the N, -seeking pole of an 
electromagnet^ the magnetis- 
ing curre7its a7-e circtdating 
round it i7i the opposite cyclic 
direction to that of the hands ^^^' ^^^' 

of a clock. Fig. 115 shows this graphically. These 
rules are true, no matter whether the beginning of the 
coils . is at the end near the observer, or at the farther 





2SS ELEMENTARY LESSONS ON [cmap. v. 

end from him, z\e. whether the spiral be a right-handed 
bcrew, or (as in Fig, 114) a left-handed screw. It will 
be just the same thing, so far as the magnetising power 
is concerned, if the coils begin at one end and run to 
the other and back to where they began ; or they may 
begin half-way along the bar and run to one end and 
then back to the other : the one important thing to know 
is which way the current flows round the bar when you 
look at it end-on. 

327. Oonstruction of Electromagnets. — The 
most useful form of electromagnet is that in which the 

iron core is bent into the 
form of a horse-shoe, so that 
both poles may be applied 
to one iron armature. In 
this case it is usual to divide 
the coils into two parts wound 
on bobbins, as in Figs. 116 
and 117. The electromagnet 
depicted in Fig. 117 is of a 
form adapted for laboratory 
experim.ents, and has mov- 
^^^* ^^^' able coils which are slipped 

on over the iron cores. A special form of electromagnet 
devised by RuhmkorfF for experiments on diamagnetism 
is shown in Fig. 127. The great usefulness of the 
electromagnet in its application to electric bells and 
telegraphic instruments Res in the fact that i/s mngnet- 
ism is under the control of the acrrentj when circuit is 
" made '^ it becomes a magnet, when circuit is *^ broken " 
it ceases to act as a magnet. 

Many special forms of electromagnet have been de- 
vised for special purposes. To give a very powerful 
attraction at very short distances, a short cylindrical 
electromagnet surrounded by an outer iron tube, united 
at the bottom by iron to the iron core, is found best. 
To give a gentle, pull over' a long range a solenoid (Art, 




:hap. v.] electricity AND MAGNETISM. 



1289 



329), having a long movable iron core is used. For 
giving a very quick -acting magnet the coils should not 
be wound all along the iron, but only round the poles. 
As a rule the iron parts, including the yoke and arma- 




Fig. 117. 

ture, should form as nearly as possible a closed magnetic 
circuit. The cross-sections of yokes should be thicker 
than those of the cores, 

328. Lifting-power of Electromagnets. — The 
lifting-power of an electromagnet depends not only on its 
"magnetic strength,'^ but also upon its form, and on the 
shape of its poles, and on the form of the soft iron 
armature which it attracts. It should be so arranged 
that as many lines of force as possible should run through 
the armature, and the armature itself should contain a 



290 ELEMENTARY LESSONS ON [chap. v. 

sufficient mass of iron. Joule designed a powerful electro- 
magnet, capable of supporting over a ton. The maximum 
attraction he could produce between an electromagnet 
and its armature was 200 lbs. per square inch, or about 
13,800.000 dynes per square centimetre. Bidwell has 
found the attraction to go up to 226*3 lbs. per square 
inch when the wrought iron core was saturated up to 
19,820 magnetic lines to the square centimetre. It can 
be shown that, when the iron is far from saturation, the 
attraction of an annat^cre of soft iron is proportional 
to the square of the *' magnetic strength " of the electro- 
magnet; for, suppose an electromagnet to have its strength 
doubled, it will induce the opposite kind of magnetisa- 
tion twice as strongly as before in the iron armature, 
and the resulting force (which is proportional to the 
product of the two strengths) will be four times as great 
as at first. 

329. Solenoid. — Without any central bar of iron or 
steel a spiral coil of wire traversed by a current acts as 
an electromagnet (though not so powerfully as when an 
iron core is placed in it). Such a coil is sometimes 
termed a solenoid. A bolenoid has two poles and a 

neutral equatorial 
region. Ampere 
found that it will 
attract magnets and 
be attracted by mag- 
nets. It will attract 
another solenoid; it 
Las a magnetic field 
Fig. iTs.^ - -- -^ resembling gene- 
rally that of a bar 
magnet If so arranged that it can turn round a vertical 
axis, it will set itself in a North and South direction 
along the magnetic meridian. Fig. i j8 shows a solenoid 
arranged with pivots, by which it can be suspended to a 
" table," like that shown in Fig. 121. 




CHAP, v.] ELECTRICITY AND MAGNETISM. 291 



Reference to Fig. 86 and to Art. 192 will recall how 
a single loop of a circuit acts as a magnetic shell of 
equivalent form and strength. A solenoid may be re- 
garded as made up of a series of such magnetic shells 
placed upon one another, all their N.-seeking faces being 
turned the same way. Since the same quantity of 
electricity flows round each loop of the spiral coil the 
loops will be of equal magnetic strength, and the total 
magnetic strength of the solenoid will be just in propor- 
tion ,16 the number of turns in the coil ; and if there be 
n turns, the number of magnetic lines of force running 
through the .solenoid will ' be 7z times as great as the 
■numbei?» due to one single turn. The use of ihe iroij 
core is by its greater magnetic induction to concentrate 
and increase the available number of lines of force at 
definite poles. The student has been told (Art. 191) 
that the lines of force due to a current flowing in a wire 
are closed curves, approximately circles (see Figl 85), 
round the wire. If there \yere no iron core many of 
these Httle circular lines of force would simply remain as 
small closed curves around their own wire 5 ' but, since 
iron has a high coefficient of magnetic induction, where 
the wiie passes near an iron core the lines offeree alter 
their shape, and instead of being little circles around the 
separate wires, run through the iron core from end 'fo 
end, and round outside from one pole back to the 
other, as in a steel magnet. Kfew of the lines of force 
do this when there is no iron ; almost all of them^do this 
when there is iron. Hence the electromagnet with its 
iron core has enormously stronger poles than the Spiral 
coils of the circuit would have alone. 

In a long straight solenoid without an iron core it is 
easy to calculate approximately the intensity of the mag- 
netic field produced by the current. For, as we have 
seen in Art. 319, the work done on a unit magnetic pole 
in moving it (against the magnetic forces) ^long.a path 
which threads through the circuit n times i^equal to ^irni 



292 ELEMENTARY LESSONS ON [chap. v. 

fergs, where the current i is expressed in absolute units 
(Art. 196). But since the work done on a unit pole 
measures the magnetic potential (Art. 3 1 o), we may say 
that the difference of magnetic potential between one 
end and the other of the long solenoid is equal to ^-khi. 
But when the magnetic potential changes as you go 
along a line, the rate of change of potential per unit of 
length is a measure of the magnetic force (Art. 310, e). 
If / be the length of the solenoid in centimetres then 
d^irni -7- / will be the intensity of the magnetic force in- 
side the solenoid. And since the intensity of the mag- 
netic force is the same thing as the intensity of the 
magnetic field at that point, we may say that this num- 
ber represents the number of lines of magnetic force per 
square centimetre of the cross-section of the solenoid. 
If H stands for the intensity of the field thus produced 
inside the solenoid, and if the radius of the spirals be r, 
and the whole number of magnetic lines N running 
through the solenoid from end to end v/ill be equal 
H X T:r\ Hence we have — 

H (inside solenoid) = f^f^ 

N (through solenoid) = irr^ x —^^ ; 

and since (see Art. 312) 47r magnetic lines go to one 
unit of magnetism, the solenoid will act as if it had at 
its ends as the amount of magnetism m in its poles — 

If the current is expressed in amperes — for which 
we may use the letter C — we must remember that ten 
amperes equal one absolute unit (Art. 196), and there- 
fore C -r 10 = /. The formulae will then become — 

10/ ' 



ctiAP. v.] ELECTRICITY AND MAGNETISM. 



293 



N 



/// = 



10/ 



It will be noticed that for any solenoid of given length 
and radius the three magnetic quantities H (interior 
magnetic force), N (total magnetic lines), and m (strength 
of poles) are proportional to the amperes of current and 
to the number of turns in the coil. The product Cn 
which thus comes into all solenoid formulas is ofteii 
referred to as the number of ampere-turns. 

330. The Laws of the Electromagnet. — The 
exact laws governing the electromagnet are somewhat 
complicated ; but it is easy to give certain rules which 
are approximately true. The current circulating in the 
coils exercises a magnetising force, and this magnetising 
force produces in the iron core a certain' amount of 
magnetism. But the amount of magnetism produced 
in the core depends on many other things beside the 
intensity of the magnetising force ; for instance, it de- 
pends on the 

quality of the '" g 

iron, on its sec- 
tional area, and 
on its length 
and form. The 
data respecting 
magnetic per- 
meability and 
saturation of 
iron in Art. 313 
are all-import- 
ant. Every 
electromagnet 
shows the same general set of facts — ^^that with small 
exciting currents there is little magnetism produced, with 
larger exciting power there is more magnetism, and that 




Q 

Fig. 118 {bis). 



294 ELEMENTARY LESSONS ON [chap. V, 

with very great exciting power the iron becomes practi- 
cally saturated and will take up very little additional 
magnetism. The curve given in Fig. 1 1 8 {bis) is char- 
acteristic of the relation between exciting power and the 
resulting magnetism. The numbers of amperes of cur- 
rent C (or, if preferred, the number of ampere-turns Cn) 
are plotted out horizontally to scale, and the correspond- 
ing amount of magnetism m vertically. For example, 
when the exciting current has the value indicated to scale 
by the length of the line GO, the amount of magnetism 
was found to be such, on its scale, as to be represented 
by the length OP. The point P is a point on the curve. 
It begins at O, no magnetism when there is no current ; 
then it rises steeply and obliquely for some time, then 
bends over and at S becomes nearly horizontal, the iron 
being nearly saturated. The dotted curve corresponds 
to ^the values of magnetism found when the exciting 
xnirrent is gradually decreased. It will be noted that 
when the current is reduced to zero there is still some 
magnetism left. Many attempts have been made 
to represent by algebraic formulae the facts that are 
thus graphically exhibited. Some of these deserve 
mention. 

Formula of Lenz and Jacobi, — According to Lenz 
and Jacobi the magnetism of an electromagnet is pro- 
portional to the current and lo the 7iufnber of turns of 
wire in the coil — in other words, is proportional to the 
amj^lre4urns. Or .in symbols — 

m = anQ^ 

where ^ is a constant depending on the quantity, quality, 
and form of iron. This rule is, however, only true 
whe^i the iron core is still far from being ^' saturated.'' 
If the iron is already strongly lAagnetised — as at P in 
the Fig. — a current twice as strong will not double the 
magnetisation in the iron. Joule in 1847 showed this 
tendency to depart from a simples- proportion. 



CHAP, v.] ELECTRICITY AND MAGNETISM. 295 

Formula of Miiller. — Miiller gave the following 
approximate rule: — The strength of an electromagnet 
is proportional to the angle whose tangent is the strength 
of the magnetising curre7it; or 

m = A tan-i C, 

where C is the magnetising current, and A a constant 
depending on the construction of the particular magnet. 
If the student will look at Fig. 90 and imagine the 
divisions of the horizontal tangent line OT to represent 
strengths of current, and the number of degrees of arc 
intercepted by the oblique lines to represent strengths 
of magnetism, he will see that even if OT be made in- 
finitely long, the intercepted angle can never exceed 90'. 
Formula of Lamont dnd Frolich. — A simpler ex- 
pression, and one more easy for algebraic calculation 
has lately come into use, and forms the basis of Frolich's 
calculations about dynamo-electric machines. We may 
write it thus : — 

where M and b are constants depending on the form, 
quality, and quantity of the iron, and on the winding of 
the coil. The constant b is the reciprocal of that number 
of amperes ^vhich would make m equal to half possible 
maximum of magnetism. Another form of this equation 
is — 



m = B 



I + (TIlC ' 



wherein B is a constant depending on the construction 
and the quality of the iron^ and c another constant (a 
small fraction) depending on the quality and quantity of 
the iron, and equal to the reciprocal of that number of 
ampere-turns which would bring the mapneusm ud to 
half-saturation. 

Yet another form of this equation is of use to express 



Hg^ ELEMENTARY LESSONS ON [chap. v. 

the number of magnetic lines N proceeding from the 
pole of the electromagnet — 

C 



N = Y 



C + C' 



where Y represents the maximum number of magnetic 
lines that there would be if the magnetising current 
were indefinitely increased and the iron core saturated, 
and C stands for that number of amperes which would 
bring the magnetism up to half-saturation. 

Hopkinson s Formula, — Hopkinson has shown that it 
is possible to calculate N by a process resembling the 
calculations made according to Ohm's law for electric 
circuits. We may look upon the iron cores and the 
armature of an electromagnet as constituting, together 
with the spaces between, a sort of magnetic circuit 
traversed by the magnetic lines. Just as we can cal- 
culate in an electric circuit the amount of current when 
we know the electromotive-force and the electric resist- 
ance round the circuit, so in a magnetic circuit we can 
calculate N if we know the magnetomotive-force (or 
the line-integral of the magnetising forces acting round 
the circuit) and the several resistances of the different 
parts of the circuit. Now the magnetomotive -force is 
equal to (see Arts. 319, d^ and 329) /^ttCh -~ 10. The 
magnetic resistance of any magnetic conductor is pro- 
portional to its length, and inversely proportional to its 
sectional area and to its permeability. Suppose then 
v/e have a magnetic circuit made up of three parts — a 
curved iron core of length Z^, section s^^ and permeability 
/Xj ; an armature of length /g, section s^^ and permeability 
/Xg ; two air-gaps between them, of length (from iron to 
iron) of /g, section (equal to area of polar surface) ^3, 
and of unit permeability (for air, /x = i) ; then the re- 
sistances of these three parts will be respectively 

10—^+10—^+—. 



^JHAP. v.] ELECTRICITY AND MAGNETISM. 297 



Then dividing the magnetomotive-force by the total 
magnetic resistance we get — 






giving the number of magnetic lines of the magnet in 
terms of the ampere-turns of excitation. It is necessary, 
however, to know the values of /x of the various pieces 
of iron at the various stages of excitation. Hopkinson 
has applied this formula with great success in calcula- 
tions about dynamo-electric machines. Analogous for- 
mulae have been used by Rowland and by Kapp. 

It may be noted that when electromagnets are wound 
with many turns of fine wire, these coils will add to the 
electric resistance of the circuit, and will tend to diminish 
the current. This has an important bearing on the 
construction of telegraphic and other instruments ; for 
while electromagnets with "long coils," consisting of 
many turns of fine v/ire, must be used on long circuits 
where there is great resistance, such an instrument 
would be of no service in a circuit of very small resist- 
ance, for the resistance of a long thin coil would be 
disproportionately great f here a short coil of few turns 
of stout wire would be appropriate. (See Art. 352.) 

As the magnetism, of the magnet depends on the 
number of ampere-turns, it should make no matter 
whether the coils are bigger than the core or whether 
they enwrap it quite closely. If there were no magnetic 
leakage this would be true in one sense : but it wastes 
more battery power to drive the current round coils of 
larger diameter, because of the greater resistance of the 
greater length of wire. Hence in well -constructed 
electromagnets tVe coils are all wound as closely to the 
iron core as is consistent with* good insulation. Also 
the iron is chosen as thick as possible^ as permeable as 



298 FXEMFNTARY LESSONS ON Ichap. v. 

possible, and forming as compact a magnetic circuit as 
possible, so that the magnetic resistance may be reduced 
to its utmost, giving the greatest amount of magnetism 
for the number of amp^re-tums of excitation. This is 
why horse-shoe-shaped electiomagnets are more powerful 
than straight electromagnets of equal weight. 

It requires time to magnetise an iron core. This is 
partly due to the fact that a current, when the circuit is 
first made, does not instantly attain its full strength, 
being retarded by the self-induced counter-electromotive- 
force (Art. 404) ; it is paitly due to the presence of 
transient reverse induction currents (Art. 393) in the 
iron itself. Faraday's large electromagnet at the Royal 
Institution takes about two seconds to attain its maxi- 
mum stiength. The electromagnets of large dynamo 
machines often take ten minutes or more to rise to their 
working stage of magnetisation. 



Lesson XXVIL — Electrodynamics. 

331. Electrodynamics. — In 1821, almost immedi- 
ately after Oerstedt's discovery of the action of a current 
on a magnet, Ampere discovered that a current acts 
upon another current, attracting it^ or repelling it 
according to certain definite laws. These actions he 
investigated by experiment, and from the experiments 
he built up a theory of the force exerted by one current 
on another. That part of the science which is con- 
cerned with the force which one current exerts upon 
another he termed Electrodjrnamics. 

332. La'ws of Parallel and Oblique Circuits. — 
The following are the laws discovered by Ampere : — 

1 It would be more correct to speak of the force as* acting on c^nducio?^ 
caKiying cu^^ents^ than as acting on the current^ themselves. It is disputed 
whether the current in the conductor is attracted; we know only with 
certainty that the conductor iUelf experiences a force. See, however, 
Art. 337' 



CHAP, v.] ELECTRICITY AND MAGNETISM. 



299 



(i.) Two parallel portions of a circuit attract one 
another if the currents in them are flowing in the same 
direction^ and repel one another if the currents flow in 
opposite directions. 

This law is true whether the parallel wires be parts 
of two different circuits or .parts of the same 
circuit. The separate turns of a spiral coil, like 
Fig. 1 185 for example, when traversed by a 
current attract one another because the current 
moves in the same direction in adjacent parts of 
the circuit ; such a coil, therefore, shortens when 
a current is sent through it, 

(ii.) Two portions of circuits crossing one another 
obliquely attract one another if both the currents run 
either towards or from the point of crossings and repel 
one another if one runs to and the other front that 
point. 

Fig. 1 1 9 gives three cases of attraction and two of 
repulsion that occur in these laws. 

(iii.) When an demerit of a circuit exerts a force on 
another element 
of a circuity that 
force always 
tends to urge the 
latter in a direc- 
tion at right 
angles to its own 
direction. Thus, 
in the case of two 
parallel circuits,, 
the force of at- 
traction or repul- 
sion acts at right- 





Fig. 119. 



angles to the currents themselves. 

An example of laws ii. and iii. is afforded by the 
case shown in Fis:. 120. Here two currents ab 



300 



ELEMENTARY LESSONS ON [chap. v. 



and cd Sive movable round O as a centre. There 
will be repulsion between a and d and between c 

and 3, while !%n the 




Fig. 120. 



Other quadrants there 
will be attraction^ a 
attracting c^ and b at- 
tracting d. 

The foregoing laws 
may be summed up in 



one, by saying that two portions of circuits, how- 
ever situated, experience a mutual force tending 
to set them so that their currents flow as nearly 
in the same path as possible. 

(iv.) The force exerted between two parallel J>ortions 
of circuits is proportional to the product of the strengths 
of the two currents^ to the length of the portions^ and 
inversely proportional to the distance between the^n. 

333. Ampere's Table. — In order to observe these 




Fig. 121. 



attractions and repulsions, Ampere devised the piece of 
apparatus known^^s Ampere's Table ^ shown in Fig. 121, 



CHAP, v.] ELECTRICITY AND MAGNETISM. 30! 

consisting of a double supporting stand, upon which 
conductors formed of wire, shaped in different ways, can 
be^hung in such a way as to be capable of rotation. 
In the figure a si^iple loop is shown as hung upon the 
supports. The ends of the wires of the movable 
portion dip into two mercury cups so as to ensure good 
contact. The solenoid, Fig. 118, is intended to be hung 
upon the same stand. 

By the aid of this piece of apparatus Ampere further 
demonstrated the following points : — 

(a) A circuit doubled back upon itself, so that the 
current flows back along a path close to itself, 
exerts no force upon external points. 

(6) A circuit bent into zig-zags or sinuosities, pro- 
duces the same magnetic effects on a neigh- 
bouring piece of circuit as if it were straight. 

(c) There is in no ca§e any force tending to move a 
conductor in the direction of its own length. 

(ti) The force between two conductors of any form is 
.he same, whatever the linear size of the system, 
provided the distances be increased in the same 
proportion, and ^that the currents remain the 
same in strength. 

The particular case, given in Fig. 122, will show the 
K^lue of these experiments; Let AB and CD represent 
two wires carrying currents, lying neither parallel nor in 
the same plane. 'It follows from (^), that if we replace 
the portion PQ by the crooked wire PRSQ, the force 
will remain the, same. The portion PR is drawn verti- 
cally downwards, and, as it can, by (c)^ experience no 
force in the direction of its length, this portion will 
neither be attracted nor repelled by CD. In the portion 
RS the current runs at right angles to CD, and this 
portion is neither attracted nor repelled by CD. In the 
portion SQ the ciirrent runs parallel to CD, and in the 
same direction, and will therefore be attracted down- 



302 



ELEMENTARY LESSONS ON [chap. v. 



wards.. On the whole, therefore, PQ will be urged to- 
wards CD. The portions PR and RS will experience 
forrfts of rotation ho\/even P beine ureed round R as a 



WarClS V_*JV. X lie pui tlV^llO X XN. ailU. XVO VVAAJI \^^^\^xi. 

forces of rotation ho\/ever, P being urged round R 




Fig 122. 

centre towards C, and R being urged horizontally round 
S towards C. These actions would tend to make AB 
parallel with^^CD. 

334. Ampere's Theory. — From he four preceding 
experimental data, Ampere built up an elaborate mathc^ 
matical theory, assuming that, in the case of these forces 
acting apparently at a distance across empty space, the 
action took place in straight lines between two points, 
the total attraction being calculated as the sum of the 
separate attractions on all the different parts. The 
researches of Faraday have, h Dwever, led to other views, 
and we now regard the mutual attractions and repulsions 
of currents as being due to actions taking place in the 
medium which fills the space around and between the 
conductors. That space we regard rather as being full 
of curving '" lines of force." Every wire carrying a 
current has a magnetic field, like that of Fig. 85, sur- 
rounding it ; and every closed circuit acts as a magnetic 
shell; Hence all these electrodynamic actions are 
capable of being regarded as magnetic actions, and they 
can be predicted beforehand for any particular case on 
that sCipposition. Thus, the author of these Lessons 



CHAP, v.] ELECTRICITY AND MAGNETISM. 303 

has shown^ that in the case of two parallel concurrent 
circuits the ^* lines of force " due to the two systems 
run into one another, embracing both circuits, while in 
the case of two parallel and non-concurrent circuits the 
" lines of force " due to the two currents indicate mutual 
repulsion. The theory of Maxwell, that a voltaic circuit 
acts like a magnetic shell (a direct deduction from Fara- 
day's work), is in practice a more fruitful conception than 
that of Ampere. On Maxwell's theory two circuits will 
tend, like two magnetic shells, to move so as to include 
as many of one another's! ^Hines of force " as possible 
(Art. 193 and 320). This will be the case when they 
coincide as nearly as possible ; /.^., when the two wires 
are parallel in every part, and when the currents run 
round in the same direction. In fact, all the electro- 
dynamic laws of parallel and oblique circuits can be 
deduced from Maxwell's theory in the simplest manner. 
An interesting experiment, showing an apparent 
mutual self-repulsion between contiguous portions of the 
circuit, was devised by Ampere. A trough divided by 
a partition into two parts, and made of non-conducting 
materials, is filled with mercury. Upon . it floats a 



Fig. 123. 

metallic bridge formed of a tent wire, of the form shown 
in Fig. 123, or consisting of a glass tube filled siphon- 
wise with mercury. When a current is sent through 
the floating conductor from X ovqr MN, and out at, 

X,Philosophkftl Magazine i November 1878, p. .3^8. 



304 ELELIENTARY LESSONS ON [chap. v. 



Y, the floating bridge is observed to move so as to 
increase tlie length of the circuit. But Maxwell has 
shown that the true explanation depends upon the self- 
induction (Art. 404) of the two parallel portions of the 
floating conductor, and that the force would be diminished 
indefinitely if the two parallel parts could be made to 
lie quite close to one another. 

335. Electromagnetic Rotations. — Continuous 
rotation can be produced bet^^een a magnet and a 
circuit, or between two parts of one circuit, provided 
that one part of the circuit can move while another part 
remains fixed, or that the current in one part can be 
leversed. The latter device is adopted in the construc- 
tion of the eleclromagnetic engiiies described in Art. 375 ; 
the former alternative is applied in a good many interest- 
ing pieces of apparatus for showing rotations, a sliding- 
contact being made between one part of the circuit and 
another. Several different forms of rotation-apparatus 
were devised by Faraday and by Ampere. One of the 
simplest of these is shown in Fig. 124, in which a 




current rising through a and passing through the lightly 
pivoted wire b V in either direction, passes down into 
a circular trough containing mercury. The trough is 
made of copper, and is connected with a wire which is 
also wound in a coil round the outside of the trough, 



CHAP, v.] ELECTRICITY AND MAGNETISM. 305 

and which forms part of the circuit. The arrows show 
the direction of the currents. The currents in the 
circular coils constitute a magnetic shell, whose N. -seek- 
ing face is uppermost. The lines of force due to this 
shell therefore run vertically in an upward direction. 
According to the converse to Ampere's Rule (Art. 186), 
a man swimming in one of the honzontal branches 
from the centre a outwards, and looking along the lines 
of force, i.e. turned on to his back, so as to look upwards, 
will be carried, along with the conductor, toward his left 
hand. And the pivoted conductor as seen from above 
will rotate continuously in the same sense as the hands 
of a clock around the centre a. A pole of a magnet 
can also be made to rotate round a current ; and if a 
vertical magnet be pivoted so as to turn around its 
own axis it will rotate when a current is led into its 
middle region and out at either end. If the current is 
led in at one end and out at the other there will be no 
rotation, since the two poles will thus be urged to rotate 
in opposite ways, which is impossible. Liquid con- 
ductors too can exhibit electromagnetic rotations. Let a 
'Cylindrical metallic vessel connected to one pole of a 
battery be filled with mercury or dilute acid, and let 
a wire from the other pole dip into its middle, so that 
a current may flow radially from the centre to the 
circumference, or vice versa; then, if this be placed 
upon the pole of a powerful magnet, or if a magnet 
be held vertically over it, the liquid may be seen to 
rotate. 

336. Electrodsmamometer. — Weber devised an 
instrument known as an electrodynamometer for measur- 
ing the strength of currents by means of the electro- 
dynamic action of one part of the circuit upon another part. 
It is in fact a sort of galvanometer, in which, instead of 
a needle, there is a small coil suspended. One form of 
this instrument, in which both the large outer and small 
inner coils consist of two parallel coils of many turns, is 

X 



3o6a 



ELEMENTARY LESSONS ON [chap. y. 



shown in Fig. 12 Sr The inner coil CD is suspended with 
its axis at right angles to that of the outer coils AA, BB^ 
and is supported bifilarly (see Art. 118) by two fine 

metal wires. If 
one current flows 
round both cofCis^in 
either direction tko 
inner bobbin tends 
to turn and set its 
coils parallel to 
the outer coils ; 
the sine of the 
angle through 
which the sus- 
pending wires are 
twisted being pro- 
portional to the 
I square of the 
' strength of the cur- 
rent. The chief 
advantage of this 
instrument over a 
galvanometer is, 
that it may be used for Induction-currents in which there 
are very rapid alternations, — a darrent in one direction 
being followed by a reverse current, perhaps thousands of 
times in a minute. Such currents hardly affect a galvano- 
meter needle at all, because of the slowness of its swing. 
Siemens employs an electrodynamometer with coils 
made of very thick wire for the absolute measurement 
of strong currents, such as are used in producing 
electric light. It is possible also to use an electro- 
dynamometer as a "Power-meter" to measure the 
electric horse power evolved by a battery or consumed 
in an electric lamp or machine. In this case the whole 
current is. sent through a fixed coil of thick wire, while 
the movable coil^ made of many turns of thin wire, is 




Fig. 125. 



CHAP, v.] ELECTRICITY AND MAGNETISM. 306^^ 

connected as a shunt across the terminals of the lamp 
or machine being thus traversed by a current proportional 
to the difference of potential between those points {sec 
Art. 360 d). The sine of the angle of deflection will 
be proportional to the product of the two currents, and 
therefore, to the product of the whole current into the 
difference of potential {see Art. 378 bis\ 

337.. Electromagnetic Actions of Convection 
Currents. — According to Faraday a stream of particles 
charged with electricity acts magnetically like a true 
conduction-current. This was first proved in 1876 by 
Rowland, who found a charged disc rotated rapidly to 
act upon a magnet as a feeble circular current would do. 
Convection currents, consisting of streams of electrified 
particles, are also acted upon by magnets. The con- 
vective discharges in vacuum-tubes (Art. 292) can be 
drawn aside by a magnet, or caused to rotate around 
a magnet-pole. The ^^ brush " discharge when taking 
place in a strong magnetic field is twisted. The voltaic 
arc (Art. 371) also behaves like a flexible conductor, 
and can be attracted or repelled by a magnet. Two 
stationary positively electrified particles repel, one 
another, but two parallel currents attract one another 
(Art. 332), and if electrified particles flowing along act 
like currents, there should be an (electromagnetic) attrac- 
tion between two electrified particles moving along 
side by side through space. According to Maxwell's 
theory (Art. 390) the electrostatic repulsion will be just 
equal to the electromagnetic attraction when the particles 
move with a velocity equal to the velocity of light. 

Quite recently Hall has discovered that when a 
powerful magnet is made to act upon a current flowing 
along in a strip of very thin metal, the equipotential 
lines are no longer at right-angles to the lines of flow of 
the current in the strip. This action appears to be 
connected with the magnetic rotation of polarized light 
(Art. 3S7)> the co-efficient of this transversa thrust cf 



3o6r ELEINIENTARY LESSONS ON chap. v. 

the magnetic field on the current being feebly + in gold, 
strongly + in bismuth, and ~ in iron, and immensely 
strong negatively in tellurium. It was shown by the 
author, and about the same time by Righi, that those 
metals which manifest the Hall effect undergo a change 
in their electric resistance when placed in the magnetic 
field. 

338. Amt)ere's Theory of Magnetism. — Am- 
pere, finding that solenoids (such as Fig. ii8) act pre- 
cisely as magnets, conceived that ;all magnets are simply 
collections of currents, or that, around every individual 
molecule of a magnet an electric current is ceaselessly 
circulating. We know that such currents could not 
flow perpetually if there were any resistance to them, 
and we know that there is resistance when electricity 
flows from one molecule to another. As we know 
nothing about the interior of molecules themselves, we 
cannot assert that Ampere's supposition is impossible. 
Since a whirlpool of electricity acts like a magnet, 
there seems indeed reason to think that magnets may 
be merely made up of rotating portions of electrified 
matten 



CHAP, v.] ELECTRICITY AND MAGNEIISM. io6d 



Lesson XXVlIl.—Diamag-nefism. 



339. Diamagnetio Experiments. — In 1778 
Brugmans of Leyden observed that when a lump of 
bismuth was held near either pole of a magnet needle it 
repelled it. In 1827 Le Baillif and Becquerel observed 
that the metal antimony also could repel and be repelled 
by the pole of a magnet. In 1845 Faraday, using power- 
ful electromagnets, examined the magnetic properties 
of a large number of substances, and found that whilst a 
great many are, like iron, attracted to a magnet, others 
are feebly repelled. To distinguish between these two 
classes of bodies, he termed those which are attracted 
paramagnetic, 1 and those which are repelled diamag- 
netic. The property of being thus repelled from a magnet 
he termed diamagnetism. 

Faraday's method of experiment consisted in suspend- 
ing a small bar of the substance in a powerful magnetic 
field between the two poles of 
an electromagnet, and observing 
whether the small bar was at- 
tracted into an axial position, as 
in Fig. 126, with its length along 
the line joining the two poles, or 
whether it was repelled into an 
equatorial position, at right 
angles to the line joining the poles, 
across the lines of force of the 
field, as is shown by the position 
of the small bar in Fig 127, sus- 
pended between the poles of an electromagnet con- 
structed on Ruhmkorff's pattern. 




Fig. 126. 



1 Or simply "magnetic." Some authorities use the term " len-o- 
magnetic.'* Sidero-inagnetic would be less objectionable than this hybrid 
word. 



3o6^ 



ELEMENTARY LESSONS ON [chap. v. 




Fig. 127. 

The following are the principal substances examined 
by the method : — 



Paramagnetic. 


Diamagnetic. 


Iron. 


Bismuth. 


Nickel. 


Phosphorus 


Cobalt. 


Antimony. 


Manganese. 


Zinc. 


Chromium, 


Mercury, 


Cerium. 


Lead. 


Titanium. 


Silver. 


Platinum.^ 


Copper. 


Many oreb and salts 


Gold. 


containing the 


Water. 


above metals. 


Alcohol. 


Oxygen gas. 


Tellurium. 




Selenium. 




Sulphur. 




Thallium. 




Hydrogen gas. 




Air. 


iirhemically pure Platinum is diaf> 


ct^netk, acGordinr; to Wiedemann 



CHAP, v.l ELECTRICITY AND MAGNETISM. 306/ 

Liquids were placed in glass vessels and suspended 
between the poles of the electromagnet. Almost all 
liquids are diamagnetic, except solutions of salts of the 
magnetic metals, some of which are feebly magnetic; 
but blood is diamagnetic though it contains iron. To 
examine gases bubbles are blown with them, and watched 
as to whether they were drawn into or pushed out of 
the field. Oxygen gas was found to be magnetic ; ozone 
has recently been found to be still more strongly so. 

340. Quantitative Results. — The diamagnetic 
properties of substances may be numerically expressed 
in terms of their sttsceptibility or their permeability 
(Art. 3 1 3). For diamagnetic bodies the susceptibility k 
is negative, and therefore the permeability (/x = i + ^irk) 
is less than unity. For bismuth the value of k is 
— 0'Ooooo2 5 according to Maxwell. The repulsion of 
bismuth is immensely feebler than the attraction of iron. 
Pllicker compared the magnetic powers of equal weights 
of substances, and reckoning that of iron as one million, 
he found the following values for the "specific mag- 
netism " of bodies : — 



Iron 


+ 


1,000,000 


Lodestone Ore 


+ 


402,270 


Ferric Sulphate 


+ 


1,110 


Ferrose Sulphate 


+ 


780 


Water 


_ 


7-8 


Bismuth 


- 


23-6 



341. Apparent Diamagnetism due to sur- 
rounding Medium.— It is found that feebly magnetic 
bodies behave as if they were diamagnetic when sus- 
pended in a more highly magnetic fluid. A small glass 
tube filled with a weak solution of ferric chloride, when 
suspended in air between the poles of an electromagnet 
points axially, or is paramagnetic ; but if it be sur- 
rounded by a stronger (and therefore more magnetic) 
solution of the same substance, it points equatorially, and 
is apparently repelled like diamagnetic bodies. All that 



3o6^ ELEMENTARY LESSONS ON [chap. v. 

the equatorial pointing of a body proves then is, that it is 
less magnetic than the medium that fills the surrounding 
space. A balloon, though it possesses mass and weight, 
rises through the air in obedience to the law of gravity, 
because the medium surrounding it is more attracted 
than it is. But it is found that diamagnetic repulsion 
takes place even in a vacuum : hence it would appear 
that space itself ^ is more magnetic than the substances 
classed as diamagnetic. 

342. Diamagnetio Polarity. — At one time Faraday 
thought that diamagnetic repulsion could be explained 
on the supposition that there existed a "diamagnetic 
polarity " the reverse of the ordinary magnetic polarity. 
According to this view, which, however, Faraday him- 
self quite abandoned, a magnet, when its N. pole is pre- 
sented to the end of a bar of bismuth, induces in that 
end a N. pole (the reverse of what it would induce in a 
bar of iron or other magnetic metal), and therefore repels 
it. Weber adopted this view, and Tyndall warmly 
advocated it, especially after discovering that the repel- 
ling diamagnetic force varies as the square of the 
magnetic power employed, a law which is the counter- 
part of the law (Art. 328) of attraction due to induction. 
Many experiments have been made to establish this 
view ; and some have even imagined that- when a 
diamagnetic bar lies equatorially across a field of force, 
its east and west poles possess difTerent properties. The 
experiments named in the preceding paragraph suggest, 
however, an explanation less difficult to reconcile with 
the facts. There can be no doubt that the phenomenon 
is due to magnetic induction : and it has been pointed 
out (Art. 89) that the amount of induction which goes 
on in a medium depjends upon the magnetic inductive 
capacity (or "permeability") of that medium. Now, 
permeability expresses the number of magnetic lines 
induced in the medium for every line of magnetising force 

1 Or, possibly, the " sether " filling all space. 



CHAP, v^ ELECTRICITY AND INIAGNETISM., 306// 

applied. A certain magnetising force applied to a space 
containing air or vacuum would induce a certain number 
of magnetic lines through it. If, however, the space con- 
sidered were occupied by bismuth, the same magnetising- 
force would induce in the bismuth y^w^r '4ines of induc- 
tion " than in vacuum. But those lines which were induced 
would still run in the same general directio7i as in the 
vacuum ; not in the opposite direction^ as Weber and 
Tyndall maintain. The result of there being a less in- 
duction through diamagnetic substances can be shown 
to be that such substances will be urged from places 
where the magnetic force is strong,* to places where it is 
weaker. This is why a ball of bismuth moves away 
from a magnet, and why a little bar of bismuth between 
the conical poles of the electro-magnet (Fig. 127) turns 
equatorially so as to put its ends into the regions that 
are magnetically weaker. There is no reason to doubt 
that in a magnetic field of uniform strength a bar oi 
bismuth would point along the lines of induction. 

343. Magne - Crystallic Action. — In 1822 
Poisson predicted that a body possessing crystalline 
structure would, if magnetic at all, have different 
magnetic powers in different directions. In 1847 
Pllicker discovered that a piece of tourmaline, which 
is itself feebly paramagnetic, behaved as a diamagnetic 
body, when so hung that the axis of the crystal was 
horizontal. Faraday, repeating the experiment with a 
crystal of bismuth, found that it tended to point with 
its axis of crystallisation along the lines of the field 
axially. The magnetic force acting thus upon crystals 
by virtue of their possessing a certain structure he 
named magne-crystallic force, Pllicker endeavoured to 
connect the magne-crystallic behaviour of crystals with 
their optical behaviour, giving the following law : there 
will be either repulsion or attraction of the optic axis 
(or, in the case of bi-axial crystals, of both optic axes) 
by the poles of a magnet; and if the crystal is a 



306/ ELEAFENTARV LESSONS ON [chap, v, 

'^ negative " one [i.e. optically negative, having an extra- 
ordinary index of refraction less than its ordinary index), 
there will be lepulsion, if a *' positive" one, there will 
be attraction. Tyndall has endeavoured to show that 
this law is insufficient in not taking into account the 
paramagnetic or diamagnetic powers of the substance as 
a whole. He finds that the magne-crj^stallic axis of 
bodies is in general a7i axis of greafe'it defisity^ and thai 
if the 7/in^? itself be piiramagnetic this axis will poi?it 
axially ; if diainagnetic^ equatorially. In bodies ^^hich, 
like slate and many crystals, possess cleavage, the planes 
of cleavage are usually at right angles to the magne- 
crystallic axis. 

344. Diainagnetism of Flames. — In 1847 Ban- 
calari discovered that flames are repelled from the axial 
line joining the poles of an electromagnet, Faraday 
showed that all kinds of flames, as well as ascending 
streams of hot air and of smoke, are acted on by the 
magnet and tend to mo'se from places where the mag- 
netic forces are stiong to those where they are weaker. 
Gases (except oxygen and ozone), and hot gases especi-- 
ally, are feebly diamagnetic. But the acti\e repulsion 
and turning aside of flames may possibly be in part 
due to an electromagnetic action like that which the 
magnet exercises on the convection-current of the voltaic 
arc and on other com ection-currents. The electric pro- 
perties of flame are mentioned in Arts, 7 and 291. 



CHAP. VI.] ELECTRICITY AND MAGNETISM. 307 



CHAPTER VI. 
MEASUREMENT OF CURRENTS, ETC. 

Lesson XXIX. — Ohm^s Law and its Consequences. 

345. In Art. 180 the important law of Ohm was 
stated in the following terms: — The strength of the 
current varies directly as the electromotive -fo7'ce^ and in- 
versely as the {total) resista7tce of the circuit. 

Using the units adopted by practical electricians, and 
explained in Art. 323, we may now restate Ohm's law in 
the following definite manner : — The mnnber of amph'es 
of current flowing through a circuit is equal to the number 
of volts of electromotive force divided by the number of 
ohfns of resistance in the entire circuit. Or^ 

Current - Electromotive-force 
Resistance ' 

c =^ 

^ R' 

In practice, however, the matter is not quite so simple, 
for if a number of cells are used and the circuit be made 
up of a number of different parts through all of which 
the current must flow, we have to take into account not 
only the electromotive-forces of the cells, but their resist- 
tances, and the resistance of all the parts of the circuit. 
For example, the current may flow from the zinc plate of 
the first cell through the liquid to the copper (or carbon) 



3oa ELEMENT LESSONS ON (chap. vi. 

plate, then through a connecting wire or screw to the next 
cell, through its liquid, through the connecting screws and 
liquids of the rest of the cells, then through a wire to a 
galvanometer, then through the coils of the galvanometer, 
then perhaps through an electrolytic cell, and finally 
through a return wire to the zinc pole of the hatter)^ In 
this case there are a number of separate electromotive-forces 
all tending to produce a flow, and a number of different 
resistances, each impeding the flow and adding to the 
total resistance. If in such a case we knew the separate 
values of all the different electromotive- forces and all the 
different resistances we could calculate what the current 
would be, for it would have the value, 



^ ^ /+/'+/"+^^-|. 



_ To tal electromotive-force 
"" Total resistance 

If any one of the cells were set wrong way* round its 
electromotive-force would oppose that of the other cells ; 
an opposing electromotive-force must therefore be sub- 
tracted, or reckoned as negative fn the algebraic sum. 
The ** polarisation " (Arts. 163 and 413) which occurs 
in battery cells and in electrolytic cells after working for 
some time is an opposing electromotive - force, and 
diminishes the total of the electromotive -forces in the 
circuit. So, also, the induced back-current which is set 
up when a current from a battery drives a magneto- 
electric engine (Art. 377) reduces the strength of the 
working current. 

346. Conductivity and Resistance. —The term 
conductivity is sometimes used as the inverse of 

resistance ; and the reciprocal - represents the con- 
ductivity of a conductor whose resistance is r ohms. In 
practice, however, it is more usual to speak of the 
resistances of conductors- than of their conductivities. 



ZHAB. VI. 1^ ELECTRICITY AND MAGNETISM. 309 

347. ILavrs of Resistance. — Resistances in a cir- 
cuit may be of two kinds— -/frj/, the resistances of the 
conductors themselves ; second^ the resistances due to 
impei'fect contact at points. The latter kind of resistance 
is affected by- pressure, for when the surfaces of two 
conductors are brought into more intimate contact with 
one another, ^. the current 'passes more freely from one 
conductor to the other. The contact-resistance of two 
co])per conductors may vary from infinity down to a 
small fraction of an ohm, according to the pressure. 
The variation of resistance at a point of imperfect con- 
tact is utilised in Telephone Transmitters (Arts. 434, 
436). The following are the laws of the resistance of 
conductors : — 

i. The 7'esisfance of a conducting wire is proportional 
to its lejtgth. If the resistance of a mile of 
telegraph wire be 13 ohms, that of fifty miles 
will be 50 X 13 = 650 ohms. 
ii. 77/^? resistance of a conducting wire is invej'sely 
proportional to the a7'ea of its cross sectio7i^ and 
therefore in the usual round wires is inversely 
proportional to the square of its diameter. Ordi- 
nary telegraph wire is about Jth of an inch thick ; 
a wire twice as thick would conduct four times as 
well, having four times the area of cross section : 
hence an equal length of it would have only |th 
the resistance, 
iii. The 7'esistance of a conducti7ig wire op given length 
and thichtcss depends upo7i the material of which 
it is made, — that is to say, upon the specific 
resistance of the material. 
348. Specific Resistance. — The specific resistance 
of a substance is best stated as the resistance in 
** absolute" C.G.S. units {i.e, in thousand millionths of 
an ohm) of a centimetre cube of the substance. The 
following Table also give^ the relative conductivity when 
that of silver is taien as 1 00. 



310 



ELEMENTARY LESSONS ON [chap. vi. 



TABLE OF SPECIFIC RESISTANCE. 



Substance. 


Specific Resistance 

(microhms of 

I cm. cube). 


Relative Conductivity. 


Metals. 
Silver 
Copper 
Gold 

Iron (soft 
Lead 

German Silver 
Mercury (liquid) 
Selenium (annealed 


1,609 
1,642 

2,154 
9,827 

19,847 
21,170 
96,146 

6 X lo^^ 


100 
96 

74 

16 

8 

7-5 
1-6 

1 


40*000.000.000 


Liquids. 

Pure Water ) 
at 22^0 i 

Dilute H2SO4 { 
(tS acid) i 

Dilute H2SO4 \ 
(\ acid) i 


7-18 X \o^^ 
•332 X lO^O 
•126 X ioi<> 


less than one 
millionth part. 


Insulators* 

Glass (at 200'^c) 
Guttapercha 
(at 20 'c) 


22.7 X 10^^ 
3-5 X Io23 


less than one 
billionth. 



It is found that those substances that possess a high 
conducting power for electricity are also the best con- 
ductors of heat. Liquids are worse conductors than the 
metals, and gases are perfect non-conductors, except 
when so rarefied as to admit of discharge by convection 
through them (Art. 283). 

349. Effects of Heat on Resistsmce.— Changes 
of temperature ' affect temporarily the conducting power 
of metals. Forbes fwnd the resistance of iron to 
increase -considerably as the temperature is raided. The 
resistances of copper and lead also increase, while that 




CHAP, vi.] ELECTRICITY AND MAGNETISM. 311 

of carbon appears on the other hand to diminish on 
heating. German-sih^er and other alloys do not show 
so much change, hence Jthey are used in making standard 
resistance-coils. Those liquids which only conduct by 
being electrolysed (Art. 205), conduct better as the 
temperature rises. The effect of light in varying the 
resistance of selenium is stated in Art. 389. 

350. Typical Circuit. — Let us consider the typical 
case of the circuit shown 
in Fig. 128, in which a 
battery, ZC, is joined up 
in circuit with a galvano- 
meter by means of wires 
whose resistance is R. 
The total electromotive- 
force of the battery we 
will call E, and the total ^'ig- ^^s- 

internal resistance of the liquids in the cells r. The 
resistance of the galvanometer coils may be called G. 
Then, by Ohm's law : — 

R + r 4- G 
The internal resistance r of the liquids of the battery 
bears a very important relation to the external resistance 
of the circuit (including R and G), for on* this relation 
depends the best way of arranging the battery cells 
for any particular purpose. Suppose, for example, 
that we have a battery of 50 small Daniell's cells at 
our disposal, of which we may reckon the electro- 
motive-force as one volt (or more accurately, 1*079 volt) 
each, and each having an internal resistance of two 
ohms. If we have to use these cells on a circuit where 
there is already of necessity a high resistance, we should 
couple them up " in simple series " rather than in 
parallel branches of a compound circuit. For, suppos- 
ing we have to send our current through a line of 
telegraph loo miles long, the external resistance R will 



312 ELEMENTARY LESSONS ON [chap, vi, 

be (reckoning 13 ohms to the mile of wire) at least 
1300 ohms. Through this resistance a single such cell 
would give a current of less than one milli-ampfere, for 
here E = i, R = 1300, r =• 2, and therefore 

C = p ^ = — \- = -^ of an ampere, a current far 

is. + r 1300 + 2 1302 * ' 

too weak to work a telegraph instrument. 

With fifty such cells in series we should have E = 50, 
r = 100, and then 

C = — ~ = -^ = -^ of an ampere, or over 3 5 milli- 

1300 + 100 1400 28 ^ ' ^ '^ 

amperes. In telegraph work, where the instruments 

require a current of 5 to i o milli-ampferes t(f work them, 

it is usual to reckon an additional DanielPs cell for every 

5 miles of line, each instrument in the circuit being 

counted as having as great a resistance as 10 miles of 

wire. 

If, however, the resistance of the external circuit be 
small, such arrangements must be made as will keep the 
total internal resistance of the battery small. Suppose, 
for example, we wish merely to heat a small piece of 
platinum wire to redness, and have stout copper wires 
to connect it with the battery. Here the external resist- 
ance may possibly not be as much as one ohm. In that 
case a single cell would give a current of J of an ampere 
(or 333 milli-amperes) through the wire, for here E = i, 
R =: I, and r = 2. But ten cells would only give half 
as much again, or 476 milli-ampferes, and fifty cells only 
495 milli-ampferes, and with an infinite number of such 
cells in series the current could not possibly be more 
than 500 milli-ampferes, because every cell, though it adds 
I to E, adds 2 to R. It is clear then that though link- 
ing many cells in series is of advantage where there is 
the resistance of a long line of wire to be overcome, yet 
where the external resistance is small the practical advan- 
tage of adding cells in series soon reaches a limit. 

But suppose in this second case, where the external 
resistance of the circuit is small, we reduce also the 



CHAP, vi.l ELECTRICITY AND MAGNETISM. S^S 



internal resistance of our batteiy by linking cells to- 
gether in parallel branches of a compound circuit, join- 
ing several zincs of several cells together, and joining 
also their copper poles together (as suggested in Art. 
i8i), a different and better result is attained. Suppose 
we thus join up four cells. Their electromotive-force 
will be no more, it is true, than that of one cell, but 
their resistance will be but ^ of one such cell, )r' J an 
ohm. These four cells would give a current of 666 
milli-amp^res through an external resistance of i ohm, 
for if E ±: I, R = I, and the internal resistance be ^ 
of r, or = J, then 
C = g-~— = f of an ampere, or 666 milli-ampferes. 

351. Best Q-rouping of Cells. — It is at once 
evident that if we arrange the cells of a battery in n 
files of m cells in series in each file (there being m x n 
similar cells altogether), the electromotive-force of each 
file will be m times the electromotive -force E of each 
cell, or mF, ; and the resistance of each file will be m 
times the resistance r of each cell, or mr. But there 
being n files in parallel branches the whole internal 
resistance will be only-- of the resistance of any one file, 
or will be -r, hence, by Ohm's law, such a battery would 
give as its current 

C - ^^-^ 

A 

It can be shown mathematically that, for a given battery of cells, the most 
effective way of grouping them when they are required to work through a 
given external resistance R, is so to choose /;t and «, that t^ internal 
resistance (J—^) shall equal the extei'-7tal resistance. The student should 

verify this rule by taking examples and working them out for different 
groupings of the cells. Although this arrangement gives the strongest current 
it is not the most economical ; for if the internal and external resistances be 
equal to one another, the useful work in the outer circuit and the useless 
work done in heating the cells will be equal also, half the energy being 
wasted. The greatest economy is attamed when the external resistance is 
very great as compared with the internal resistance ; only, in this case, the 
materials of the battery will be consumed slowly, and the current will not be 
drawn off at its greatest possible strength. 



314 ELEMENTARY LESSONS ON [chAp. VI. 

352. Long and Short Coil Listruments. — The student will 
also now have no difficulty in perceiving why a "long-coil" 
galvanometer, or a "long-coil" electromagnet, or instrument of 
any kind in which the conductor is a long thin wire of high 
resistance, must not be employed on circuits where both R and 
r are aheady small. He will also understand why, on circuits 
of great length, or where there is of necessity a high resistance 
and a battery of great electromotive force is employed, "short- 
coil " instruments are of little service, for though they add little 
to the resistances their few turns of wire are not enough with 
the small currents that circulate in high-resistance circuits ; and 
why " long-coil " instruments are here appropriate as multiplying 
the effects of the currents by their many turns, their resistance, 
though perhaps large, not being a serious addition to the existing 
resistances of the circuit. A galvanometer with a "long-coil " 
of high resistance, if placed as a shunt across two points of a 
circuit, will draw therefrom a current proportional to the differ- 
ence of potential between those points. Hence such an instru- 
ment may be used as a voltmeter (Art. 360 d.) 

353. Divided Circuits. — If a circuit divides, as in 
Fig. 129, into two branches at A, uniting together again 

at B, the -current will also 
be divided, part flowing 
through one branch part 
through the other. The 
relative strengths of cur- 
rent in the two branches 
will be proportional to 
their conductivities, /.^., 
^' ^^^' . inversely proportional to 

their resistances. Thus, if r be a wire of 2 ohms re- 
sistance and / 3 ohms, then current in r : current in 
/ r=^ r^ir 
= 3:2, 
or, -I of the whole current will flow through r, and f of 
the whote current through /. 

The joint resistance of the divided circuit between A 
and B will be less than the resistance of either branch 
singly, because the current has now choice of either path. 
In fact, the joint conduct! v^ity will be the sum of the two 




CHAP. VI.] ELECTRICITY AND MAGNETISM. 315 

separate conductivities. And if we call the joint resist 
ance R. it follows that 

I ^ I , £ _ r' -^ r 
'^^ r r' rr' y 

whence R = -r—^ or, in words, the joint 

resistance of a divided condtcctor is eqtial to the prodtict 
of the two separate resistances divided by their sum. 

Kirchhoft has given the following important laws, both of 
them deducible from Ohm's law. 

(i. ) In any branching network of wires the algebraic sum of 
the currents in all the wires that meet in any i>oint is 
zero, 

(ii.) When there are several electromotive -forces acting at 
different points of a circuity the total electromotive -force 
round the circuit is equal to the su77i of the 1 esistances 
of its separate parts viultiplied each into the strength of 
the current that flows thi'ough it. 

354. Current Sheets. — When a current enters a 
solid conductor it no longer flows in one line but spreads 
out and flows through the mass of the conductor. AVhen 
a current is led into a thin plate of conducting matter it 
spreads out into a ''current sheet "and flows through 
the plate in directions that depend upon the fomi of the 
plate and the position of the pole by which it returns to 
the battery. Thus, if wires from the two poles of a 
battery are brought into contact with two neighbouring 
points A and B in the middle of a very large flat sheet 
of tinfoil, the current flows through the foil not in one 
straight hne from A to B, but in curving " lines of flow," 
which start out in all directions from A, and curl round to 
meet in B, in curves very like those of the *' lines of force " 
that run from the N.-pole to the S.-pole of a magnet 
(Fig. 50). When the earth is used as a return wire to 
conduct the telegraph currents (Fig. 160), a similar 
spreading of the currents into current sheets occurs. 



ji6 ELEMENTARY LESSONS ON [chap, vu 



Lesson XXX. — Electrical Measurements. 

355. The prax:tical electrician has to measure electri- 
cal resistances, electromotive -forces, and the capacities 
of condensers. Each of these several quantities is 
measured by comparison with ascertained standards, the 
particular methods of comparison varying, however, to 
meet the circumstances of the case. Only a few simple 
cases can be here explained. 

356. Measurement of Resistance. — Resistance 
is that which stops the flow of electricity. Ohm's law 
shows us that the strength of a current due to an electro- 
motive force falls off in proportion as the resistance in 
the circuit increases. 

{ci) It is therefore possible to compare two resistances 
with one another by finding out in what proportion each 
of them will cause the current of a constant battery to 
fall off. Thus, suppose in Fig. 128 we have a standard 
battery of a few DanielPs cells, joined up in circuit with 
a wire of an unknown resistance R, and with a galvan- 
ometer, we shall obtain a current of a certain strength, 
as indicated by the galvanometer needle experiencing a 
certain deflection. If we remove the wire R, and sub- 
stitute in its place in the circuit wires whose resistances 
we knoWy we may, by trying, find one which, when inter- 
posed in the path of the current, gives the same deflection 
on the galvanometer. Hence we shall know that this 
wire and the one we called R offer equal resistance to 
the current. Such a process of comparison, which we 
may call a method of substitution of equivalent resistances, 
was further developed by Wheatstone, Jacobi, and others, 
when they proposed to employ as a standard resistance 
a long thin wire coiled upon a wooden cylinder, so that 
any desired length of the standard wire might be thrown 
into the circuit by unwinding the proper number of turns 
of wire off" the cylinder, or by making contact at some 
pomt at any desired distance from the end of the wire. 



CHAP. VI.] ELECTRICITY AND MAGNETISM. 317 

Such an instrument was known as a Rheostat, but it is 
now superseded by the resistance coils explained below. 

(3) The method explained above can be used with , 
any galvanometer of sufficient sensitiveness, but if a 
tangent galvanometer is available the process may be 
shortened by calculation. Suppose the tangent galvano- 
meter and an unknown resistance R to be included in 
the circuit, as in Fig. 128, and that the current is strong 
enough to produce a deflection of d degrees : Now sub- 
stitute for R any known resistance R', which will alter the 
deflection to d' ; then (provided the other resistances of 
the circuit be negligibly small) it is clear that since the 
strengths of the currents are proportional to ^an d and 
fan d' respectively, the resistance R can be calculated by 
the inverse proportion. 

fan d : fan 5' ^ R' : R. 

(c) With a differential galvanometer (Art. 203), and a 
set of standard resistance coils, it is easy to measure the 
resistance of a conductor. Let the circuit divide into two 
branches, so that part of the current flows through the 
unknown resistance and roimd one set of coils of the 
galvanometer, the other part of the current being made 
to flow through the known resistances and then round 
the other set of coils in the opposing direction. When 
we have succeeded in matching the unknown resistance 
by one equal to it from amongst the known resistances, 
the currents in the two branches will be equal, and the 
needle of the differential galvanometer will show no 
deflection. With an accurate instrument this null method 
is very reliable. 

(d) The best of all the ways of measuring resistances 
is, however, with a set of standard resistance coils and 
the important instrument known as Wheatstone's Bridge, 
described below in Art. 358. 

(e) To measure very high resistances the plan may be 
adopted of charging a condenser from a standard battery 
for a definite period through the resistance, and then 



3i8 ELEMENTARY LESSONS ON fcHAP. vi. 

ascertaining the accumulated charge by discharging it 
through a ballistic galvanometer (Art. 204), 

357. Fall of Potential along a Wire.— To tmderstand the 
principle of Wheatstone's Bridge we must explain a preliminary 
point. If the electric potential of different points of a circuit 
be examined by means of an electrometer, as explained in Art. 
263, it is found to decrease all the way round the circuit from 
the + pole of the battery, where it is highest, down to -• pole, 
where it is lowest*. If the circuit consist of one wire of uniform 
thickness, which offers, consequently, a uniform resistance to 
the current, it is found that the potential falls uniformly; if 
however, part of the circuit resists more than another, it is 
found that the potential falls most rapidly along the conductor 
of greatest resistance. But in every case the fall of potential 
between any two points is proportional to the resistance between 
those two points ; and we know, for example, that when we 
have gone round the circuit to a point where the potential has 
fallen through half its value, the current has at that point gone 
through half the resistances. The difference of potential e be- 
tween the poles of a battery (of electromotive-force E and 
internal resistance r) in a circuit of which the fotal resistance is 
R + r, may be written in the following ways as : 

358. Wheatstone's Bridge. — This instrument, 
invented by Christie, and applied by Wheatstone to 
measure resistances, consists of a system of conductors 
shown in diagram in Fig. 130. The circuit of a constant 
battery is made to branch at P into two parts, which 
re-unite at Q, so that part of the current flows through 
the point M, the other part through the point N. The 
four conductors D, C, B, A, are spoken of as the " arms " 
of the " balance " or " bridge ;^' it is by the proportion 
subsisting between their resistances that the resistance 
of one of them can be calculated when the resistances of 
the other three are known. When the current which 
starts from C at the battery arrives at P, the potential 
will have fallen to a certain value. The potential of the 
current in the upper branch falls again to M, and 
continues to fall to Q. The potential of the lower 



CHAP. VI.] ELECTRICITY AND MAGNETISM. 



319 



branch falls to N, and again falls till it reaches the value 
at Q. Now if N 'be the same proportionate distance 




Fig. 130. 

along the resistances between P and Q, as M is along 
the resistances of the upper line between P and Q, the 
potential will have fallen at N to the same value as it 
has fallen to at M ; or, in other words, if the ratio of the 
resistance C to the resistance D be equal to the ratio 
between the resistance A and the resistance B, then M 
and N will be at equal potentials. To find out whether 
they are at equal potentials a sensitive galvanometer is 
placed in a branch wire between M and N ; it will show 
no deflexion when M and N are at equal potentials ; or 
when the four resistances of the arms " balance " one 
another by being in proportion, thus : — 

A:C::B:D. 
If, then, we know what A, B, and C are, we can calculate 
D, which will be B x C 



D = 



Example.— Thus if A and C are (as in Fig. 133) 10 oMms 
and 100 ohms respectively, and B be 15 ohms^ D will 
be IS X 100 -5- 10 = 150 (fhms^ 



320 



ELEMENTARY LESSONS ON [chap. vi. 



359. Resistance Coils.— ^ Wires of standard resist- 
ance are now sold by instrument makers under the name 
of Resistance Ooils. They consist of coils of german- 
silver (see Art. 349) (or sometimes silver-iridium alloy), 
wound with great care, and adjusted to such a length as 
to have resistances of a definite number oi olwis. In order 

to avoid self-induction, 
and the consequent sparks 
(see Art. 404) at the 
opening or closing of the 
circuit, they are wound 
in the peculiar manner 
indicated in Fig. 131,, 
each wire (covered with 
Fig. 131. silk or paraffined -cotton) 

being doubled pn itself 
before being coiled up. Each end of a coil is soldered 
to a solid brass piece, as coil i to A and B, coil 2 to 
B and C ; the brass pieces being themselves fixed to a 
block of ebonite (forming the top of the "resistance 
box"), with sufficient room between them to admit of 
the insertion of stout well-fitting plugs of brass. Fig. 
132 shows a complete resistance-box, as fitted up for 





Fig. 132. 



electrical testing, with the plugs in their places. So 
long as the plugs remain in, the current flows through 



CHAP. VI.] ELECTRICITY AND MAGNETISM. 



321 



the selid brass pieces and plugs without encountering 
any serious resistance ; but when any plug is removed, 
the current can only pass from the one brass piece to 
the other by traversing the coil thus thrown into circuit. 
The series of coils chosen is usually of the following 
numbers of ohiiis^ resistance — i, 2, 2, 5 ;. 10, 20, 20, 

50; 100, 200, 200, 500 ; up to 10,000 ohms. 

By pulling out one plug any one of these can be thrown 
into the circuit, and any desired whole number, up to 
20,000, can be made up by pulling out more plugs ; thus 
a resistance of 263 olnns will be made up as 200 -r 50 
+ 10 + 2 4- I. 

It is usual to construct Wheatstone's bridges with some 
resistance coils in the arms A and C, as well as with a 
complete set in the arm B. The advantage of this 




Fig. 133. 



arrangement is that by adjusting A and C we determine 
the proportionality between B and D, and can, in certain 
cases, measure to fractions of an ohm. Fig. 133 shows 
a more complete scheme, in which resistances of 10, 100, 
,and 1000 ohms are included in the arms A and C, 



322 ELEMENTARY LESSONS ON fCHAP. vi. 

Example. — Suppose we had a wire, wnose resistance we 

knew to be between 46 and 47 ohms^ and wished to 

measure the fraction of an oh7n^ we should insert it at D, 

and make A 100 ohms and C lo ohms ; in that case D 

would be balanced by a resistance in B 10 times as great 

as the wire D. If, on trial, this be found to be 464 ohms 

we know that D = 464 x lo ^ log = 46*4 ohms. 

In practice the bridge is seldom or never made in the 

lozenge -shape of the diagrams. The resistance-box of 

Fig. 132 is, in itself, a complete "bridge," the appropriate 

connections being made by screws at various points. In 

using the' bridge the battery circuit should always be 

completed by depressing the key K^ before the key 

Kg of the galvanometer circuit is depressed, in order 

to avoid the sudden violent " throw " of the galvanometer 

needle, which occurs on closing circuit in consequence of 

self-induction (Art. 404). 

360. Measurement of Eleotromotive-Poroe. — 
There being no easy absolute method of measuring 
electromotive-forces, thfey are usually measured relatively^ 
by comparison with the electromotive-force of a standard 
cell, such as that of Daniell (Art. 170), or better still 
that of Latimer Clark (Art. 177). The methods of 
comparison are various ; only four can here be men- 
tioned. 

[a) Call E the electromotive-force of the battery to be 
measured, and E' that of a standard battery. Join E 
with a galvanometer, and let it produce a deflection of 
^1 degrees through the resistances of the circuit ; then 
add enough resistance r to bring down the deflection to 
^2 degrees — say 10 degrees less than before. Now 
substitute the standard battery in the circuit and adjust 
the resistances till the deflection is \ as before, and then 
add enough resistance /, to bring down the deflection 
to Sg. Then 

r' : ^ = E' : E, 
s'nce the resistances that will reduce the strength of the 
current equally will be proportional to the electromotive- 
forces 



CHAP. VI.] ELECTRICITY AND MAGNETISM. 323 



(d) If the poles of a standard battery are joined by a long 
thin wire, the potential will fall uniformly from the + to 
the — pole. Hence, by making contacts at one pole 
said at a point any desired distance along the wire, any 
desired proportional part of the whole electromotive-force 
can be taken. This proportional part may be balanced 
against the electromotive-force of any other battery, or 
used to compare the difference between the electromotive- 
forces of two different cells. 

[c) The electromotive-force of a battery may be measured 
directly as a difference of potentials by a quadrant electro- 
meter. In this case the circuit is never closed, and no 
current flows, 

(d) If a galvanometer be constructed so that the resistance 
of its coils is several thousand ohms, in comparison with 
which the internal resistance of a battery or dynamo 
machine is insignificant, such a galvanometer will serve 
to measure electromotive-forces ; for, by Ohm's law, the 
strength of current which such a battery or dynamo can 
send through it will depend only on the electromotive- 
force between the ends of the coil. Such a galvanometer, 
suitably graduated, is sometimes called a ** Voli -meter "^^ 
or ^^ Potential galvanometer^^ It can be used to determine 
the difference of potential between any two points of a 
circuit by connecting its terminals as a shunt to the 
circuit between these two points. 

361. Measurenient of Internal Resistance of 
Battery. — This may'Se done in three ways. 

(p) Note by a tangent galvanometer the strength of the 
current, first, when the resistance of the external circuit 
is small ; and secondly, when a larger known external 
resistance is introduced. From this the proportion 
between the internal resistance and the introduced ex- 
ternal resistance can be calculated. 

(3) {Method of Opposition), — Take two similar cells and 
join them in opposition to one another, so that they send 
no current of their own. Then measure their united 
resistance just as the resistance of a wire is measured. 
The resistance of one cell will be half that of the two. 

\c) (Manc^s Method), — Place the cell itself in one arm of 
the Wheatstone's bridge, and put a key where the battery 
usually is, adjust the resistances till the permanent galvano- 



324 ELEMENTARY LESSONS ON [chap. Vl. 

meter deflection is the same whether the key be depressed 
or not. When this condition of things is attained the 
battery resistance is balanced hy those of the other three 
arms. {A^of a reliable method.^ 
862. Measurement of Capacity of a Con- 
denser. — The capacity of a condenser may be measured 
by comparing it with the capacity of a standard con- 
denser—such as the -J microfarad condenser shown in 
Fig. 1 06, — in one of the following ways : — 

{a) Charge the condenser of unknown capacity to a 
certain potential ; then make it share its charge Avith the 
condenser of known capacity, and measure the potential 
to which the charge sinks : then calculate the original 
capacity, which will bear the same ratio to the joint 
capacity of the two as the final potential bears to the 
original potential. 

{b) Charge each condenser to equal differences of 
potential, and then discharge each successively through 
a ballistic galvanometer (Art. 204), when the sine of half 
the angle of the first swing of the needle will be propor- 
tional in each case to the charge, and therefore to the 
capacity. 

(c) Charge the two condensers simultaneously from 
one pole of the same battery, interposing high resistances 
in each branch, and adjusted so that the potential rises 
at an equal rate in both; then the capacities are inversely 
proportional to the resistances through which they are 
respectively being charged. 

{d) Another method, requiring no standard condenser. 
is as follows : — Allow the condenser. \Aliose capacity is to 
be measured, to discharge itself slowly through a wire of 
ver)' high resistance. The time taken by the potential 
to fall to any given fraction of its ori/inal value is pro- 
portional to the resistance, to the capacity, and to the 
logarithm of the given fraction, 

363. Hesistance Expressed as a Velocity. — It will be 
seen, on reference to the table of " Dimenjions '* of electro- 
magnetic units (Art. 324), that the dimensions of resistance art* 



CHAP. VI.] ELECTRICITY AND MAGNETISjNI. 



325 



given as LT~^, which are the same dimensions (see Art. 258) as 
those of a velocity. Every resistance is capable of being 
expressed as a velocity. The following considerations may 
assist the student in forming a physical conception of this : — 
Suppose we have a circuit composed of two horizontal rails 




(Fig. 134), CS and DT, i centim. apart, joined at CD, and 
completed by means of a sliding piece AB. Let this variable 
' circuit be placed in a uniform magnetic field of unit intensity, 
the lines of force being directed vertically downwards through 
the circuit. If, now, the slider be moved along towards ST 
with a velocity of n centimetres per second, the number of 
additional lines of force embraced by the circuit will increase at 
the rate n per second ; or, in other words, there will be an 
induced electromotive - force (Art. 394) impressed upon the 
circuit, which will cause a current to flow through the slider 
from A to B. Let the rails have no resistance, then the 
strength of the current will depend on the resistance of AB. 
Now let AB move at such a rate that the current shall be of 
unit strength. If its resistance be one "absolute" (electro- 
magnetic) imit it need only move at the rate of i centim. per 
second. If its resistance be greater it must move with a pro- 
portionately greater velocity ; the velocity at which it must 
move to keep up a current of unit strength being numerically 
equal to its resistance. The resistance known as ^' one ohm " is 
intended to be 10^ absolute electromagnetic units y and therefore is 
represented by a velocity of 10^ centimetres, or te7t million metres 
(one earth -quadrant) per second, 

564. Evaluation of the Ohm.— The value of the ohm in absolute measure 
was determined by a Committee of the British Association in London in 1863* 
It being impracticable to give to a horizontal sliding -piece so high a velocity 
as was necessitated, the velocity which corresponded to the resistance of a 
wire was measured in the following way: — A ring of wire (of many turns), 
pivoted about a vertical axis, as in Fig. 135, was made to rotate very rapidly 
and uniformly. Such a ring in rotating cuts the lines of force of the earth's 
magnetism. The northern half of the ring, in moving from west toward ease 



326 



ELEMENTARY LESSONS ON 



[CHAF VI. 




will have (see Rule Art. 395) an upward current induced in it, while the 
southern ,haif, in crossing from east toward west, will have a downward 

current induced in it. Hence the 
rotating ring will, as it spins, act 
as its own galvanometer if a small 
magnet he hung at its middle ; the 
magnetic effect due to the rotating 
coil being proportional directly to 
the horizontal component of the 
earth's magnetism, to the velocity 
of rotation, and to the number of 
turns of wire in the coil, and in- 
versel}^ proportional to the resist- 
ance of the wire of the coils. Hence, 
all the other data being known, the 
resistance can be calculated and 
measured ns a velocity. The 
existhig ohms or B.A, units were constructed b}'" comparison with this 
rotating coil ; but there being some doubt as to whether the B,A. unit really 
represented lo^ centims. per second, a redetermination of the ohm was 
suggested in 1880 by the British Association Committee. 

364 (bis). The Legal Ohm— At the International Congress of Electricians 
in Paris 1881 the project for a redetermination of the ohm was endorsed, and 
it was also agreed that the practical standard? should no longer be con- 
structed rn German silver wire, but that thej- should be made upon the plan 
originally suggested bj- Siemens, by defining \hQ pi-actical ohm as the resist- 
ance of a column of pure mercur\' of a ceitain length, and of one millimetre 
of cross-section. The original " Siemens' unit " was a colimm of mercury 
one metre in length, and one square millimetre in section, and was rather 
less than an ohm (0*9415 B.A. unit). Acting on measurements made by the 
1 est phj'sicists of Europe, the Paris Congress of 1884 decided that the 
mercury* column representing the legal ohm shall be 106 centimetres in 
length. [I ord Rayleigh's deteimination gave 106*21 centimetres of mercury, 
as representing the true theoretical ohm (= lo^ absolute units).] Our old 
B.A. ohm i«? onl^- 0*9887 of the new legal ohm ; and our old volt is 0*9887 of 
the lega^ volt* 



NOTE ON THE RATIO OF THE ELECTROSTATIC TO THE 
ELECTRO]\lAGNKTIC UNITS. 

365. If the student \^ ill compare the Table of Dimensions of Electrostatic 
Units of Alt. 258 with that of the Dimensions of Electromagnetic Units of 
Art. 324, ha will observe that the dimensions assigned to similar units are 
different \v. the two systems. Thus, the dimensions of *^ Quantity" in 
ehctroHaiic measure are ISP L^ T , and in electromagveiic measure arc 
M2 L^* Dividing the former by the latter we get LT"*^' a quantity which 



CHAP. vi.J ELECTRICITY AND MAGNETISM. 



327 



we at cnce see is of the nature of a velociif. This velocity occurs in every 
case in the ratio of the electrostatic to the electromagnetic measure of every 
unit. It is a definite concrete velocity, and represents that velocity at which 
two electrified particles must travel along side by side in order that their 
mutual electromagnetic attraction (considered as equivalent in moving to 
two parallel currents) shall just equal their mutual electrostatic repulsion, 
see Art 337. This velocity, " v" which is of enormous importance in the 
electromagnetic theory of light (Art. 390), has been measured in several ways. 



Unit. 


Electrostatic. 


Electeomagne ric. 


Ratio 


Quantity . 
Potential . 
Capacity 
Resistance . 


M* L* T-1 

M* L^ T-i 

L 

L-i T 


M^ L^ 
M* L* T-2 

LT-i 


L2T-2 = ^ 
L-2 T^ = I5 



{a) Weber and Kohlrausch measured the electrostatic unit of quantity 
and compared it with the electromagnetic unit of quantity, and found the ratio 
«/ to be = 3*1074 X iqI^ centims. per second.* 

{b) Sir W. Thomson compared the two units of potential and found 

V = 2*825 X iol<>, 
and later, = ^'93 X lolO. 

(<r) Professor Clerk Maxwell balanced a force of electrostatic attraction 
against one of electromagnetic repulsion, and found 

V = 2-88 X lolO. 

{d) Professors Ayrton and Perr^' measured the capacity of a condenser 
electromagnetically by discharging it into a ballistic galvanometer, and 
electrostatically by calculations from its size, and found 

V = 2*980 X lolO. 

(e) Professor Joseph J. Thomson compared the capacity of a condenser 
as measured electrostatically by calculation and as measured electromag* 
netically on a Wheatstone's bridge, and deduced 

V = 2*963 X lo^O, 
The velocity of light is believed to be = 2*9992 X lol^ ; 

or, according to G. Forbes's latest determination, 

the velocity of r^</ light is 2*9826 X lol^. 

Assuming as a mean value 3 X lo^O, and comparing with Arts. 257 and 323, 
we get : — 

I coulomb = 3X io9 electrostatic (C.G.S.) units of quantity ; 
I volt = JXio-2 electrostatic (C.G.S.) units of potential ; 
I farad = 9X iqII electrostatic (C.G.S.) units of capacity ; 
I ohm = ^Xio-11 electrostatic (C.G.S.) units of resistance. 



32S ELEMENTARY LESSONS ON [chap, vih 



CHAPTER VII 

HEAT, LIGHT, AND WORK, FROM ELECTRIC CURRENTS. 

Lesson XXXL — Heating Effects of Currents. 

366. Heat and Besistance. — A current may do 
work of various kinds, chemical, magnetic, mechanical, 
and thermal. In every case where a current does work 
that work is done by the expenditure of part of the energy 
of the current. We have seen that, by the law of Ohm, 
the current produced by a given battery is diminished in 
strength by anything that increases the external resistance. 
But the strength of the current may be diminished, in 
certain cases, by another cause, namelj", the setting up 
of an opposing electromotive force at some point of the 
circuit. Thus, in passing a current through a voltameter 
(Art. 214) there is a diminution due to the resistance of 
the A oltameter itself, and a further diminution due to the 
opposing electromotive -force (commonly referred to as 
" polarisation ") which is generated while the chemical 
work is being done. So, again, when a current is used to 
drive an electromagnetic motor (Art. 375), the rotation 
of the motor will itself generate a back -current, which 
will diminish the strength of the current. Whatever 
current is, however, not expended in this way in external 
work, \^ frittered down into heat, either in the battery or 
in some part of the circuit, or in both. Suppose a 
quantity of electricity to be set flowing round a closed 
circuit. If there were no resistance to stop it it would 



CHAP. VTI.3 ELECTRICITY AND MAGNETISM. 



329 



ciiculate for ever; just as a waggon set rolling along a 
circular railway should go round for ever if it were not 
stopped by friction. When matter in motion is stopped 
by fiiction the energ)'' of its motion is frittered down by 
the friction into heat. When electricity in motion is 
stopped bj^ resistance the energj' of its flow is frittered 
do\\n by the resistance into heat. Heat, in fact, appears 
wherever the circuit offers a resistance to the current. 
If the teiminals of a battery be joined by a short thick 
wire of small resistance, most of the heat will be de- 
veloped in the battery ; whereas, if a thin wire of con- 
siderable resistance be interposed in the outer circuit, it 
will grow hot, while the battery itself will remain com- 
paratively cool. 

367. Laws of Development of Heat: Joule's 
Law. — ^To investigate the 
development of heat by a 
current. Joule and Lenz used 
instruments on the prin- 
ciple of Fig. 136, in which 
a thin wire joined to two 
stout conductors is enclosed 
within a glass vessel con- 
taining alcohol, into which 
also a thermometer dips. 
The resistance of the wire 
being known, its relation to 
the other resistances can 
be calculated. Joule found 
that f/ie mimbej' of tintts of heat developed in a con- 
ducto7' is proportional — 

(i.) to its resistance : 

(ii.) to the square of the strength of the current ; 
and 

(iii.) to the time that the current lasts. 
The equation expressing these relations is known as 
Joule's Law, and is — 

Z 




Fig. 136. 



330 ELEMENTARY LESSONS ON [cHAt>. viL 

H = CRt X 0-24 
where C is the current in amperes, R the resistance in 
ohms, / the time in seconds, and H the heat in the usual 
unit af heat-quantities, viz. the amount of heat that will 
raise i gramme of water through I'^C of temperature 
(Art. 2 55). 

Joule's law may be arrived at by the following calculation. 
The work W done by a current in moving Q units of electricity 
through a difference of potential V^ - Vi is — 

W = Q{V,~Vx); 
and since Q = Ct, and V^ - V^ = E, and W = JH, (where J is 
Joule's equivalent = 4-2 x lo^ and H the heat in water-gramme- 
centigrade degree units), we have — 

JH =± CtE (and E = CR). 

= C2Rt 

whence H = —j—* 
But as C and R are here in " absolute " units, they must be 
multiplied by 10 -2 x lo^ = lo^, to reduce to the ordinary case 
of amperes and ohms ; whence— 

H = C^Rt -7- 4-2 
= C^Rt X 0-24. 

This is equivalent to the statement that a current of 
one ampere flowing through a resistance of one ohm 
deve lopes therein 0-24 heat-units per second. 

Dr. Siemens proposed to call this quantity of heat (or its 
mechanical equivalent in work) by the name of one joule. This 
suggestion was adopted; the electric unit of heat, ih.^ joule, is 
therefore 0*24 of an ordinary heat-unit or calorie (Art. 255), and i 
calorie is equal to \' 2 joules. 

The second of the above laws, that the 'heat is, ccetens paribus^ propor- 
tional to the square, of the strength of the current, often puzzles young 
students, who expedt the heat to be proportional to the current simply. 
Such may remember that the consumption of ^zinc is, cateris paribus ^ also 
proportional to the square of the current; for, suppose that in working 
through a high resistance (so as to get all the heat developed outside the 
battery) we double the current by doubling the number of battery cells, there 
will be twice as much zinc consumed as before in eachc^t and as there are 
twice as many cells as at first the c.onsumption of zinc is four times as great 
as before. 

368. Fa vre s Experiments. — 'Favre made a series of mast 
imjportant experiments on the relation of the energy of a current 



CHAP. VII.] ELECTRICITY AND MAGNETISM. 331 

to the heat it developes. He agcertaiiied that the number of 
heat-units evolved when 33 grammes (i equivalent) of zinc are 
dissolved in dilute sulphuric acid (from which it causes hydrogen 
to be given off) to be 18,682. This figure was arrived at by 
conducting the operation in a vessel placed in a cavity of his 
calorimeter, an instrument resembling a gigantic thermometer 
filled with mercury, the expansion of which was proportional to 
the heat imparted to it. When a Smee's cell was introduced 
into the same instrument, the solution of the same amount of 
zinc was observed to be accompanied by the evolution of 18,674 
units of heat (/.^. an amount almost identical with that observed 
before), and this amount was the same v/hether the evolution 
look place in the battery-cell when the circuit was closed with a 
short thick wire, or whether it took place in a long thin wire 
placed in the external circuit. He then arranged 5 Smee's cells 
in series, in cavities of the calorimeter, and sent their current 
round a small electromagnetic engine. The amount of heat 
evolved during the solution of 33 grammes of zinc was then 
Dbserved in three cases ; (i.) when the engine was at rest ; (ii.) 
ivben the engine was running round and doing no work beyond 
overcoming the friction of its pivots ; (iii.) when the engine was 
employed in doing 13,124,000 gramme-centimetres (= 12,874 
X 10^ ergs) of work, by raising a weight by a cord running over 
a pulley. The amounts of heat evolved in the circuit in the 
three cases were respectively, 18,667, 18,657, and 18,374 imits. 
In the last case the work done accounts for the diminution in 
the lieat frittered down in the circuit. If we add the heat- 
^uivalent of the work done to the heat evolved in the latter 
case, we ought to get the same value as before. Dividing the 
12,874 X 10^ ergs oi work by Joule's equivalent, expressed m 
"absolute" measure (42 x lo^), we get as the heat- equivalent of 
the work done 306 heat units. Now 18,374 -i- 306 = 18,680, 
a quantity which is almost identical with that of the first 
observation, and quite within the limits of unavoidable experi- 
mental error. 

369. Bise of Temperatiire. — The elevation of 
temperature in a resisting wire depends on the nature of 
the resistance. A very short length of a very thin wire may 
resist just as much as a long length of stout wire. Each 
will cause the same number of units of heat to be evolved, 
but in the former case, as the b&at is spent in warming a 



$72 ELEMENTARY LESSONS ON [chap, vn^ 

short thin wire of small mass, it will get very hot, whereas 
in the latter case it will perhaps only warm to an imper- 
ceptible degree the mass of the long thick wire. If the 
wire weigh zc/ grammes, and have a specific capacity for 
hQzt.s, then H = siadj where 6 is the rise of tempera- 
ture in degrees (Centigrade). Hence 

n C2R/ • 

= 0-24 X • 

sw 

Since the resistance of metals increases as they rise in 
temperature, a thin wire heated by the current will resist 
more, and grow hotter and hotter until its rate of loss of 
heat by conduction and radiation into the ' surrounding 
air equals the rate at which heat is supplied by the 
current. 

The following pretty experiment illustrates the laws of 
heating. The current from a few cells is sent through a 
chain made of alternate links of silver and platinum 
wires. The platinum links glow red-hot while the silver 
links remain comparatively cool. The explanation is 
that the specific resistance of platinum is about six times' 
that of silver, and its capacity for heat about half as 
great ; hence the rise of temperature in wires of equal 
thickness traversed by the same current is roughly twelve 
times as great for platinum as for silver. 

, Th'u wires heat much more rapidly than thick, i^Ae 
rise of temperature in different parts of the same wire 
(carrying the same current), beings for different thick- 
nesses, inversely proportional to the fourth power of the 
diameters. 

Thus, suppose a wire at any point to become reduced to halj 
its diameter, the cross-section will have an area J as great as in 
the thicker part. The resistance here will be 4 times as great, 
and the numbet of heat units developed will be 4 times as great 
as in an equal length of the thicker wire. But 4 times the 
amount of heat spent on \ the amount of *metal will warm it to 
a degree 16 times as great, and 16 = 2i 

For surgical purposes a thin platinum wire, heated 
red-hot by a current, is sometimes used instead of a 



CHAP. VII.] ELECTRICITY AND MAGNETISM^ 333 

knife, as, for example, in the operation of amputating the 
tongue for cancer. Platinum is chosen on account of its 
infusibility, but even platinum wires are fused by the 
current if too strong. Carbon alone, of conductors, resists 
fusion. 

370. Blasting by Electricity. — In consequence of 
these heating effects, electricity can be applied to fire 
blasts and mines, stout conducting wires being carried 
from an appropriate battery at a distance to a special 
fuze^ in which a very thin platinum wire is joined in the 
circuit. This wire gets hot when the current flows, and 
being laid amidst an easily combustible substance to 
serve as a priming, ignites this and sets fire to the charge 
of gunpowder. Torpedoes can thus be exploded beneath 
the water, and at any desired distance from the battery. 

The special case of heat developed or abstracted by a 
current passing through a junction of di3similar metals, 
known as Peltier's effect, is mentioned in Art. 380, 



Lesson XXXII. — The Electric Light. 

371. The Voltaic Arc. — If two pointed pieces of 
carbon are joined by wires to the terminals of a power- 
ful voltaic battery or other generator of electric currents, 
and are brought into contact for a moment and then 
drawn apart to a short distance, a kind of electric flame 
called the voltaic arc is produced between the points 
of carbon, and a brilliant light is emitted by the white 
hot points of the carbon electrodes. This phenomencai 
was first noticed by Humphry Davy in 1800, and its ex- 
planation appears to be the following : — Before contact 
the difference of potential between the points is insufficient 
to permit a spark to leap across even -^-^ of an inch of 
air-space, but when the carbons are made to touch, a 
current is established. On separating the carbons the 
momentary extra -current due. to self-induction of ihe 



334 ELEMENTARY LESSONS ON [chap. vil. 

circuit (Art 404), which possesses a high electromotive- 
force, can leap the short distance, and in doing so 
volatilises a small quantity of carbon between the points. 
Carbon vapour being a partial conductor allows the 
current to continue to flow across the gap, provided it be 
aot too wide ; but as the carbon vapour has a very high 




Fig, 137. 
resistance it becomes intensely heated by the passage 
of the current, and the carbon points also grow hot. 
Since, however, solid matter is a better radiator than 
gaseous matter, the carbon ^ i t? emit fer more light 



GHAP. VII.] ELECTRICITY AND MAGNETISM, 33s 

than the arc itself, though they are not so hot In the 
arc the most infusible substances, such as flint and 
diamond, melt ; and metals such as gold and platinum 
are even vapourised readily in its intense heat. When 
the arc is produced in the air the carbons slowly bum 
away by oxidisation. It is observed, also^ that particles 
of carbon are torn away from the + electrode, which be- 
comes hollowed out to a cup-shape, and some of these 
are deposited on the — electrode, which assumes a 
pointed form, as shown in Fig. 137. The resistance ol 
the arc may vary, according to circumstances, from 0*5 
ohm to nearly 100 ohms. It is also found that the arc 
exerts an opposing electromotive-force of its own of about 
39 volts when the arc is quiet, or 1 5 volts v/hen hissing. 
To produce an electric light satisfactorily a minimum 
electromotive-force of 40-50 voUs is necessary ; and as 
the current must be at least from 5 to 10 or more 
ampires^ it is clear that the internal resistance of the 
battery or generator must be kept small. • With weaker 
.currents or smaller electromotive-forces it is impracticable 
to maintain a steady arc. The internal resistance of 
the ordinary DanielPs or Leclanche's cells (as used in 
telegraphy) is too great to render them serviceable foi 
producing electric lights. A battery of 40-60 Grove's 
cells (Art. 171) is efficient, but will not last more than 
2 or 3 hours. A dynamo-electric machine (such as 
described in Art. 407 to 411), worked by a steam-engine, 
is the best generator of currents for practical electric 
lighting. The quantity of light emitted by an electric 
lamp is disproportionate to the strength of the current ; 
and is, within certain limits, proportional to the square 
of the heat developed, or to the fourth power of the 
strength of the cun-ent. 

372. Electric Arc Lamps. —Davy employed wood 
charcoal for electrodes to obtain the arc light. Pencils 
of hard gas-carbon . were later introduced by Foucault, 
Uk all the more recent, arc lamps, pencils of a more 



336 



ELEMENTARY LESSONS ON [chap. vii. 



dense and homogeneous artificial coke-carbon are used. 
These consume away more regularly, and less rapidly, 
but still some contrivance is necessary to push the 
points of the carbons forward as fast as 
needed. It is requisite that the mechan- 
ism should start the arc by causing the 
pencils to touch and then separate them 
to the requisite distance for the produc- 
tion of a steady arc ; the mechanism 
should also cause the carbons not only 
to be fed into the arc as fest as they 
consume, but also to approach or recede 
automatically in case the arc becomes 
too long or too short ; it should further 
bring tjie carbons together for an instant 
to start the arc again if by any chance 
the arc goes out. Electric Arc Lamps 
or Regulators^ fulfilling these 
xronditions, have been invented 
by a number of persons. These 
may be classified as follows : — 
{a) Clockwork Lamps, — ^Fig. 
138 shows the regulator of Fou- 
cault as constructed by Duboscq; 
in this lamp the carbon-holders 
are propelled by a train of 
clockwork wheels actuated by 
a spring. An electromr/jnet 
at the base, through which the 
current runs, attracts an arma- 
ture and governs the clock- 
work. If the current is too 
strong the armature is drawn down, and the clockwork 
draws the carbons further apart. If the current is 
weakened by the resistance of the arc, the armature is 
drawn upwa.rds by a spring, and a second train of wheels 
tomes into pla^ and moves the caaions nearer together. 




\ 



Hg; X38. 



CHAP. viL] ELECTRICITY AND MAGNETISM. 337 

Clockwork arc lamps have also been devised by Serrin 
and by Crompton, in which the weight of the carbon- 
holders drive the clockwork mechanism. 

(^) Break-wheel Lamps, — Jaspar and Crompton have 
devised mechanism for regulating the rate of feeding 
the carbon into the arc by adding to the train of 
wheels a break-wheel ; the break which stops the wheel 
being actuated by a small electromagnet which allows 
the wheel to run forward a little when the resistance of 
the arc increases beyond its normal amount. 

{c) Solenoid Lamps, — In this class of arc lamp one 
of the carbons is attached to an iron plunger capable of 
sliding vertically up or down inside a hollow coil or 
solenoid, which, being traversed by the current, regulated 
the position of the carbons and the length of the arc. 
Siemens employed two solenoids acting against one 
another differentially, one being a main-circuit coil, the 
other being a shunt-circuit. If the resistance of the arc 
became too great, more of the current flowed past the 
lamp through the shunt-circuit, and caused the carbon- 
holders to bring the carbons nearer together. Shunt- 
circuits to regulate the arc have also been used by 
Lontin, Brush, Lever, and others. 

(</) Clutch Lamps, — A somewhat simpler device is 
that of employing a clutch to pick up the upper carbon 
holder, the lower carbon remaining fixed. In this kind 
of lamp the clutch is worked by an electromagnet, 
through which the current passes. If the lamp goes 
out the magnet releases the clutch, and the upper carbon 
falls by its own weight and touches the lower carbon. 
Instantly the current starts round the electromagnet, 
causes it to act on the clutch which grips the carbon- 
holder and raises it to the requisite distance. Should 
the arc grow too long the lessening attraction on the 
clutch permits the carbon -holder to advance a little. 
Hart, Brush, Weston, and Lever employ clutch lamps. 

373. Electric Candles. ^ — To obviate the expense 



338 



ELEMENTARY LESSONS ON [chap. vii. 



and complication of such regulators, electric candles have 

been suggested by Jablochkoflf, 
Wilde, and others. Fig. 139 
depicts JablochkojBTs candle^ 
consisting of two parallel pen- 
cils of hard carbon separated 
by a thin layer of plaster of 
Paris and supported in an up- 
right holder. The arc plays 
across the summit between the 
two carbon wicks. In order 
that both carbons may consume 
at equal rates, rapidly alternat- 
ing currents must be employed, 
which is disadvantageous ftt)m 
an economical point of view. 

374. Inoandesoent Elec - 
trie Lamps. — Voltaic arcs of 
an illuminating power of less 
than 100 candles cannot be 
maintained steady in practice, 
and are uneconomical. For 
small lights it is both simpler and cheaper to employ a 
thin continuous wire or filament of some infusible con- 
ductor, heated to whiteness by passing a current through 
it Thin wires of platinum have repeatedly been sug- 
gested for this purpose, but they cannot be kept from 
risk of fusing. Iridium wires and thm strips of carbon 
hav€ also been suggested by many inventors. Edison in 
1878 devised a lamp consisting of a platinum spiral com- 
bined with a short-circjiiting switch to divert the current 
from the lamp in case it became overheated. More recently 
thin filaments of carbon have been e^mployed by Swan, 
Edison, Lane-Fox, Maxim, Crookes, and others for the 
construction of little incandescem lamps. In these lamps 
the carbon filament is mounted upon conducting wires, 
usually of platinum, which pass into a glass bulb, into 




*'»g- 139. 



CHAP. VIL] ELECTRICITY AND MAGNETISM. 



339 



which they are sealed, the bulbs b'eing afterwards ex- 
hausted of air and other gases, the vacuum being made 
very perfect by the employment of special mercurial 
air-pumps. Carbon is better for this purpose than 
platinum or any other metal, partly because of its 
superior infusibility and higher resistance, and partly 
because of the remarkable property of carbon of offering 
a lower resistance when hot than when cold. This 
property, which is the reverse of that observed in metals, 
renders it less 
liable to become 
overheated. 
The forms of 
several incan- 
descent lamps 
are shown in 
Fig. 140. Swan 
( I ) prepares his 
filament from 
cotton thread 
parchmentised 
in sulphuric 
acid and after- 
wards carbon- 
ised ; such a 
filament be- 
coming remark- 
ably elastic and 
metal-like in the process. 




Fig. 140 



Edison (2) now uses a thin 
flat strip of carbonised bamboo instead of a filament. 
Maxim (3) uses a preparation of paper. Lane-Fox (4) 
and Akester (6) use prepared and carbonised vegetable 
fibres. Crookes (5) employs a filament made from animal 
or vegetable matter parchmentised by treatment with 
cuprammonic chloride. The resistance of such lamps 
varies according to size and length of the filament from 
3 to 200 ohms* The current necessary to heat the 



340 ELEMENTARY LESSONS ON [chap. Vil, 

filaments white-hot is usually from i to i -3 amplre. To 
produce this current the electromotive force that must 
be applied is dependent on the resistance of the lamp. 
Suppose a lamp the resistance of which is 60 ohms when 
cold and 40 ohms when hot : the requisite current will 
be obtained by applying an electromotive force of about 
50 volts^ because 50 -^ 40 = 1*25 amph^e. The best 
economy is obtained with very thin cylindrical filaments 
of high resistance. Flat strips of- carbon which expose 
a disproportionate amount of surface, and thick iilaments 
in which the mass of carbon is considerable, are open 
to objection. Well-made lamps, if not overheated, will 
last 1000 to 1200 hours before the filament disintegrates. 
It is usual to group these lamps in parallel, arc between 
the leading main conductor and the return main, so that 
each lamp is independent of the others if the electro- 
motive force of the supply is constant. The light 
emitted varies according to the size of lamp from 2 to 
50 candles. There appears to be some difficulty in 
obtaining durable filaments that will bear being made 
Incandescent to a higher candle power. 

Lesson XXXIII. — Electromotors {Electromagnetic 
Efigines), 

375. Electromotors. — Electromagnetic engines, or 
electromotors, are machines in which the motive power; 
is derived from electric currents by means of electro- 
magnets. In 1821 Faraday showed a simple case of 
rotation produced between a magnet and a current of 
electricity. In 1831 Henry, and in 1833 Ritchie, con- 
structed electromagnetic engines producing rotation by 
electromagnetic means. Fig. 141 shows a modification 
of Ritchie's electromotor. An electromagnet DC, is 
poised upon a vertical axis between the poles of a fixed 
magnet (or electromagnet) SN. A current, generated 
by a suitable battery, is carried by wires which terminate 



CHAP. VII.] ELECTRICITY AND MAGIIETISM. 341 



in two mercury-cups, A, B, into which dip the ends of 
the coil of the movable electromagnet CD. When a 
current traverses the coil of 
CD it turns so as to set itself 
in the line between the poles 
NS, but as it swings round, 
the wires that dip into the mer- 
cury-cups pass from one cup 
to the opposite, so that, at the 
moment when C approaches S, 
the current in CD is reversed, 
and C is repelled from S and 
attracted round to N, the cur- 
rent through CD being thus 
reversed every half turn. In +> 
larger electromotors, the mer- 
cury-cup arrangement is replaced 
by a commutator, consisting of 
a brass ring, slit into two or 
more parts, and touched at ^^^* ^^i- 

opposite points by a pair of metallic springs or ^^ contact 
brushes." 

In another form of electromotor, devised by Froment, 
bars of iron fixed upon the circumference of a rotating 
cj^inder are attracted up towards an electromagnet, in 
which the current is automatically broken at the instant 
when each bar has come close up to its poles. In a third 
kind, an electromagnet is made to attract a piece of soft 
iron alternately up and down, with a motion like the 
piston of a steam-engine, which is converted by a crank 
into a rotatory motion. In these cases the difficulty 
occurs that, as the attraction of an electromagnet falls off 
nearly in inverse proportion to the square of the distance 
from its poles, the attracting force can only produce 
effective motion through very small distances. 

The dynamo-electrie machines of Gramme, Siemens, 
and others, described in Arts. 407 to 411/ will also work 




342 ELEMENTARY LESSONS ON [chap. vii. 

as electromotors, and, Indeed, are the most efficient of 
electromagnetic engines. 

In 1839 Jacobi propelled a boat along the river Neva 
at the rate of 2^ miles per hour with an electromagnetic 
engine of about one horse-power, worked by a battery of 
64 large Grove's cells. 

In 1882 an iron screw-boat capable of carrying 12 
persons, and driven by two Siemens' dynamos, with a 
power of about 3 horse-power, the electricity being fur- 
nished by 45 accumulators of the Sellon-Volckmar type, 
has been worked upon the Thames at a speed of 8 miles 
per hour. 

Electric railways on which trains are propelled by 
power furnished by djrnamo-electric generators stationed 
at some fixed point, and communicating with the electro- 
magnetic machinery of the train either by the rails or by 
a special conductor, have been constructed by Siemens 
in Berlin, and by Edison in Menlo Park. 

376. Electric Transmission of Po^wer to a 
distance. — The increasing use of dynamo -electric 
machines for electric lighting has revived the problem of 
transmitting power to a distance by electrical means, 
and so utilising waste water-power. Niagara Falls 
has been made to turn water-wheels or turbines, and 
drive dynamo-electric machines, thereby generating 
currents which can be conveyed by wires to electro- 
motors at distant points and there reconverted into 
mechanical power Whether such transmission is profit- 
able or not depends on the efficiency of the machines 
employed. 

377. Theory of Eflaciency of Electromotors. — 
If a galvanometer be included in a circuit with a battery 
and an electromotor, it is found that the current is weaker 
when the electromotor is working than when the electro- 
motor is standing still, and that the faster the electromotor 
runs the weaker does the battery current become. This 
is due to electromagnetic induction (Art. 391) between the 



CHAP. VII.] ELECTRICITY AND MAGNETISM. 343 

moving and fixed parts of the electromotor, which, as it 
spins round, generates a back-current. The electromotive- 
force due to this inductive action increases with the speed 
of the electromotor, so that the back-current is strongest 
when it runs fastest. If the motor be loaded so as to 
do work by moving slowly against considerable forces, the 
back-current will be small, and only a small proportion 
of the energy of the current will be turned into useful 
work. If it be set to run very quickly, so as to generate 
a considerable back-current, it will utilise a larger pro- 
portion of the energy of the direct current, but can only 
run fast enough to do this if its load be very light, 
Jacobi calculated that the practical efficiency lay between 
these two extremes, and that an electromotor would turn 
the energy of a battery into work in the most effective 
way when it was allowed to do its work at such a speed 
that the battery current was thereby reduced to half its 
strength. This is indeed true if it be desired to do the 
work at the quickest possible rate. But where economy 
in working is desired, and when it is not needful to get 
through the work as rapidly as possible, or to consume 
materials in the battery at a great rate, then a higher 
economic efficiency will be attained by making the electro- 
motor do lighter work and spin at a greater speed ; for 
if the electromotive-force of the battery be E volts^ and 
the counter electromotive-force of the motor while running 
be e volts ^ then the efficiency of the motor (that is to 
say, the ratio which the work it takes up from the cur- 
rent bears to the whole energy of the current) will be 
equal to -g Now if the motor be allowed to run more 
quickly e will increase proportionately, and if it runs 
very quickly e may become very nearly equal to E ; that 
is to say, the motor will utilise very nearly all the energy 
of the current. But since, by Ohm's law, the current is 
~ ' -, it follows that if e is very nearly as great as E, 



the current will be reduced to a small fraction of its 
original strength. The materials of the battery will be 



344 ELEMENTARY LESSONS ON [chap. Vil, 

more slowly used, and it will take a longer time to do 
the total amount of the work, but the perce7ttage of 
energy of the current turned into work will be higher. 
A good modern dynamo-electric machine (Art. 408) used 
as a motor can attain an efficiency of over 90 per cent. 

378. Cost of Workini^. — The cost of working 
electromotors by batteries is great. A pound of zinc 
contains only about \ as much potential energy as a 
pound of coal, and it costs more than twenty times a3 
much : the relative cost for equal amounts of energy is 
therefore about 120 : i. But, as shown above, an elec- 
tromagnetic engine .will turn 85 per cent of the electric 
energy into work, while even good steam-engines only 
turn about 10 to 20 per cent of the energy of their fuel 
into work, small steam-engines being even less efficient. 
But, reckoning electromagnetic engines as being 5 times 
as *^ efficient " as steam-engines of equal power, the 
necessary zinc is still 24 times as dear as the equivalent 
amount of coal. This calculation does not take into 
account the cost of acids of the batteries. In fact, 
where strong currents are wanted, batteries are aban- 
doned in favour of dynamo-electric machines, worked by 
steam or water power, or by gas-engines. 

In the case of transmission of power, as in the preced- 
ing paragraph, the expense may be far smaller if the 
original water-power costs little. The dynamo-machine 
may turn 90 per cent of the mechanical power into the 
energy of electric currents, and the electromotor may 
convert back 85 per cent of the current energy (or ^d 
per cent of the original power) into work. 

378. {bis) Calculation of Electric Power. ^— The 
mechanical work of ^ current may be calculated as 
follows : A current whose strength is C conveys through 
the circuit in / seconds a quantity of electricity = C/. 
But the number of ergs of work W, done by a current 
is equal to the product of the quantity of electricity into 
the difference of potentials E through which it is irans- 



CHAP. VII.] ELECTRICITY AND MAGNETISM 345 

ferred (Art. 367), provided these latter are expressed in 
"absolute'' C.G.S. units; or 

C/E=W 

Now if W ergs of work are done in / seconds, the rate of 
working is got by dividing W by Ij whence 

If C and E are expressed in amperes and volts respec- 
tively, and it is desired to give the rate of working in 
horse -power, it must be remembered that i ampere == 
10*^ C.G.S. units of current; that i volt = 10^ C.G.S. 
units of E.M.F. ; and that i horse-power (as defined by 
Watt) =550 foot-pounds per second = 76 kilogramme- 
metres per second = 76 x 10^ gramme-centimetres per 
second = 746 x 10^ ergs per second, whence 

^ajnpjre^^^ of doing work in H.-P. 

For example, to find the rate at which actual work is 
consumed in an electric lamp : measure the whole current 
in amperes J measure the difference of potential between 
the terminals of the lamp in volts j multiply them to- 
gether and divide by 746 ; the result will be the number 
of horse-power used up in the^lamp : or the rule may be 
written thus : — 

H-P = CE X 0-00134. 

A convenient " electric power-meter^^ may be made of 
an electrod)namometer (Art. 336) having the fixed coil 
of thick wire to receive the whole current, and having 
the movable coil of many turns of thin wire arranged 
as a shunt to the lamp or dynamo whose power is to be 
measured. 

It has been proposed by Preece and by Siemens to 
call the unit of electric power {i.e. one a7npere working 
through one volt) a, watt. One horse-power then equals 
746 watts. 



% A 



346 CLLMl^NTARY LtLbbONS ON [chap, viii 



CHAPTER VIII. 

THERMO-ELECTRICITY. 

Lesson XXXIV. — TliermO'Electric Currents. 

379. In 1822 Seebeck discovered that a current may 
be produced in a closed circuit by heating a point of 
contact of two dissimilar metals. Thus, if a piece of 
bismuth and a piece of antimony be soldered together, 
and their free ends be connected with a short -coil 
galvanometer, it is found that if the junction be warmed 
to a temperature higher than that of the rest of the 
circuit, a current flows whose direction across the heated 
point is from bismuth to antimony, the strength of the 
current being proportional to the excess of temperature. 
If the junction is cooled below the temperature of the 
rest of the circuit a current in the opposite direction is 
generated. "The electromotive -force thus set up will 
maintain a constant current so long as the excess of 
temperature of the heated point is kept up, heat being 
all the while absorbed in order to maintain the energy of 
the current. Such currents are called Thermo-electric 
currents, and the electromotive -force producing them 
is known as Thermo-electromotive-force, 

380. Peltier Effect. — In 1834 Peltier discovered 
a phenomenon which is the converse of that discovered 
by Seebeck. He found that if a current of electricity 
from a battery be passed through a junction of dissimilar 
metSls the junction^ is either heated or cooled, according 



CHAP. Viii.J ELECTRICITY AND MAGNETISM, 347 

to the direction of the cun-ent. Thus a^ current which 
passes through a bismuth-antimony pair in the direction 
from bismuth to antimony absorbs heat in passing the 
junction of these metals, and cools it 5 whereas, if the 
current flow from antimony to bismuth across the 
junction it evolves heat, and the junction rises in tem- 
perature. 

This phenomenon of heating (or cooling) by a cuprent, 
where it crosses the junction -of two dissimilar metals 
(known as the " Peltier effect," to distinguish it from the 
ordinary heating of a circuit where it offers a resistance 
to the current, which is sometimes called the "Joule 
effect "), is utterly different from the evolution of heat in 
a conductor of high resistance, for (a) the Peltier effect 
is reversible^ the current heating or cooling the junction 
according to its direction, whereas a current meeting 
with resistance in a thin wire heats it in whichever 
direction it moves ; and {U) the amount of heat evolved 
or absorbed in the Peltier effect is proportional simply 
to the strength of the current, not to the squa7'e of that 
strength as the heat of resistance is. 

The complete law of the heat developed in a circuit will 
therefore require to take into account any Peltier effects which 
may exist at metal junctions in the circuit. If the letter P 
stand for the difference of potential due to the heating of the 
junction, expressed as a fraction of a volt, then the complete 
law of heat is 

H =0-24 X (C2R/ + PC/) 

which the student should compare with Joule's law in Art. 367. 
The quantity called P is also kncfwn as the coefficient of the 
Peltier effect ; it has different values for difTcrent pairs of metals, 
and is numerically equal to the number of ergs of work which 
are the d)niamical equivalent of the heat evolved at a junction 
of the particular metals by the passage of one amp}re of electricity 
through the junction. 

381. Thermo-electric Laws. — The thermo-electric 
properties of a circuit are best studied by reference to 
the simple circuit of Fig. 142, which represents a 



34S 



ELEMENTARY LESSONS ON [cHAr. viii. 




Fig. 142. 



bismuth-antimony pair imited by a copper wire. Volta's 
law (Art. 72) concerning the difference of • potentials 
due to contact would tell us that when all are at one 

temperature the dif- 
ference of poten- 
tials between^bis- 
muth and copper 
in one direction 
is equal to the sum 
of the differences 
between bismuth 
and antimony, and 
between antimony 
and copper in the 
other direction, and that hence there would be equilibrium 
between the opposing and equal electromotive -forces. 
But when a junction is heated this equilibrium no longer 
exists and A^olta's law ceases to be true. The new 
electromotive-force set up at the heated junction is found 
to obey the following laws : — 

(i.) The thennO' electro motive 'force is^ for the same 
pair of metals^ proportional {e\en through con- 
siderable ranges of temperature) to the excess, of 
iemperattire of the junctio7t over the rest of the 
circuit, 
(ii.) The total therjito-electroinotive -force in a circuit 
is the su?n of all the separate thenno 'electromotive- 
forces at the various junctions. 
It follows from this law that the various metals can be 
arranged, as Seebeck found, in a series, according to 
their thermo-electric power, eaclvone in the series being 
thermo-electrically positive (as bismuth is to antimony) 
toward one lower down. The following is the thermo- 
electric series of metals, together with the differences 
of potentials (in microvolts) which they exhibit with a 
difference of temperature of i°C, lead being regarded as 
the standard zero metal. 



CHAP. VIII.] ELECTRICITY AND MAGNETISM. 349 



+ Bismuth 



89 to 97 



II7S 
o 

- 0^9 

- 37 

- 3-8 

- 17-5 

- 22*6 to — 26*4 



German-silver 

Lead 

Platinum . 

Zinc 

Copper 

Iron .... 
— Antimony , 

A very small amount of impurity may make a great 
difference in the thermo-electric power of a nietal, and 
some alloys, and some of the metallic sulphides, as 
galena, exhibit extreme thermo-electric power. 

The electromotive -forces due to heating single pairs 
of metals are very small indeed. If the junction of a 
copper-iron pair be raised i°C above the rest of the 
circuit its electromotive-force is only 137 millionth s of a 
volt {i,e. 137 microvolts). That of the more powerful 
bismuth-antimony pair is for i°C, about 117 microvolts. 

382. Thermo-electric Inversion. — Gumming dis- 
covered that in the case of iron and other metals' an 
inversion of their thermo-electric properties may take 
place at a high temperature. In the case of the copper- 
iron pair the temperature of 280° is a neutral point; 
below that temperature the current flows through the 
hotter junction from the copper to the iron ; but when 
the circuit is above that temperature iron is thermo- 
electrically positive to copper. 

383. Thermo-electric Diagram. — The facts of 
thermo-electricity are best studied by means of the 
diagram (Fig. 143) suggested by Sir W. Thomson and 
constructed by Professor Tait. The horizontal divisions 
represent temperatures, the vertical distances differences 
of potential divided by absolute temperatures, on a scale 
of millionths of volts per degree. These differences are 
measured with respect to the metal lead, which is 
taken as the standard of zero at all temperatures, because^ 
while with other metals there appears to be a difference 
of potentials between the metal hot and the same metal 



3SO 



ELEMENTARY LESSONS ON [chap. viii. 



cold, hot lead brought into contact with cold lead shows 
no perceptible difference of potential. 



V 



+ 5 



LEIAD 




-5 



-JO 



-15 



d 



o° 



too' 



200" 



300 



400" 



500 



F^ig- 143- 

An example will illustrate the usefulness of the diagram. Let 
a circuit be made by uniting at both ends a piece of iron and a 
piece of copper ; and let the two junctions be kept at 0° and 
ioo° respectively by melting ice and boiling water. Then the 
total electromotive-force round the circuit is represented by the 
area ^, o, -15, <5. The slope of the lines for the various metals 
represents the property referred to above, of an electromotive- 
force between differently heated portions of the same metal 
accompanied by an absorption or evolution of heat when the 
current flows from a hotter to a colder portion of the same 
metal. This effect, known as the Thomson effect from its 
discoverer Sir W. Thomson, is opposite in iron to what it is 
in copper or zinc. In copper, when a current of electricity flows 
from a hot to a cold point, it evolves heat in the copper, and it 
absorbs heat when it flows from a cold point to a hot point in 
the copper. In iron a current flowing froni a hot point to a 
cold point absorbs heat. 

384. Thermo-electric Piles. — In ordsr to increase 



CHAP. VIII.] ELECTRICITY AND MAGNETISM, 351 



the electromotive-force of thermo-electric pairs it is usual 
to join a number of pairs of metals (preferably bismuth 
and antimony) in series, but so bent that the alternatt 
junctions can be heated as shown in Fig. 144 at B B Bj 




Fig. 144. 

whilst the other set A A A are kept cool. The various 
electromotive-forces then all act in the same direction, 
and the current is increased in proportion to the number 
of pairs of junctions. Powerful thermo-electric batteries 
have been made by Clamond, — an iron-galena battery 
of 120 pairs affording a strong current; but it is 
extiemely difficult to maintain them in effecti\e action 
for long, as they fail after continued use, probably 
OA^ing to a permanent molecular change at the junctions. 
In the hands of Melloni the thermo-electric pile or 
thermopile, constructed of many small pairs of anti- 
mony and bismuth united in a compact form, proved an 
excellent electrical thermometer when used in conjunction 
with a sensitive short-coil astatic galvanometer like that 
of Fig. 88. For the detection of excessively small 
differences of temperature the thermopile is an invaluable 
instrument, the currents being propoitional to the differ- 



352 



ELEMENTARY LESSONS ON [chap. viii. 



ence of temperature between the hotter set of junctions 
on one face of the thermopile and the cooler set on the 
other face. The arrangement of the thermopile and 
galvanometer for this purpose is shown in Fig. 145. 




Fi^. 1 45 



CHAP. IX.] ELECTRICITY AND MAGNETISM. 353 



CHAPTER IX. 

ELECTROOPTICS. 

Lesson XXXV. — General Relations between Light 
and Electricity. 

385. Of late years several important relations have 
been observed between electricity and light. These 
relations may be classified under the following heads : — 

(i.) Production of double refraction by dielectric stress. 

(ii.) RotatTOn of plane of polarisation of a ray of light 

on traversing a transparent medium placed in a 

magnetic field, dr by reflection at the surface of a 

magnet. 

(ill.) Change of electric resistance, exhibited by 

selenium and other bodies during exposure to light 

0v.) Relation between refractive index and dielectric 

capacity of transparent bodies. 
It was announced by Mrs. Somerville; by Zantedeschi, ^d 
others, that steel needles could be magnetised by exposing 
portions of them to the action of violet and ultra-violet rays 
of light ; the observations were, however, erroneous. 

386. Electrostatic Optical Stress.— In 1875 Dr. 
Kerr of Glasgow discovered that glass when subjected to 
a severe electrostatic stress undergoes an actual strain, 
which can be olDserved by the aid of a beam of polarised 
light. In the original experiment two wres were fixed 
into holes drilled in a slab of glass, but not quite meeting, 



354 ELEMENTARY LESSONS ON [chap. IS. 

CO that when these were placed in connection with the 
terminals of an induction coil or of a Holtz machine the 
accumulating charges on the wires subjected the inter- 
vening dielectric to an electrostatic stress. The slab 
when placed between two Nicol prisms as polariser and 
anal3'seri exhibited double refraction. The behaviour of 
the glass was as if it had been subjected to a pull along 
the direction of the electric force, /.<?., as if it had ex- 
panded along the lines of electrostatic induction. Later, 
he found that bisulphide of carbon and other insulating 
liquids exhibit similar phenomena, but that of these the 
fatty oils of animal and vegetable origin exhibited an 
action in the negative direction, as if they had contracted 
along the lines of induction. It is found that the 
quanfify of optical effect (/.^., the difference of retardation 
bet\vcen the ordinary and extraordinary rays) per unit 
thickness of the dielectric is proportional to the square oj 
the resultant electric force. The axis of double refraction 
is along the line of the electric force. Quincke has 
pointed olit that these phenomena can be explained, by 
the existence of electrostatic expansions and contractions, 
stated in Art. 273. 

387. Magnet o-optio Rotation of the Plane of 
Polarisation of a Ray of Lig-ht. — A ray of light 
is said to be polarised if the vibrations take place in one 
plane. Ordinary'' light can be reduced to this condition 
by passing it through a suitable polarising apparatus 
(such as a Nicol prism, a thin slice of totirmaline crystal. 
etc.) In 1845 Faraday discovered that a ray polarised 
in a certain plane can be twisted round by the action 
of a magnet, so that the vibrations are executed in a 
dliTerent plane. The plane in which a ray is polarised 
can be detected by observing it through a second Nicol 
pwsm-(or tourmaline), for each such polariser is opaque 
to rays polarised in a plane at right angles to that plane 

1 The student is referred to Prof. Balfour Stewart's Lessons on Klement- 
ary Physics for further information concerning the properties of polarised light. 



CKAP. IX.] ELKCTRICITY AND MAGNETISM. 355 

in which it would itself polarise light. Faraday caused 
a polarised ray to pass through a piece of a certain 
^* heavy glass " (consisting chiefly of borate of lead), 
lying in a powerful magnetic field, between the poles 
of a large electromagnet, through the coils of which a 
current could be sent at pleasure. The emerging ray 
traversed a second Nicol prism which had been turned 
round until all the light was extinguished. In this posi- 
tion its ov/n plane of symmetry was at right angles to the 
plane of polarisation of the ray. On completing the cir- 
cuit, light was at once seen through the analysing Nicol 
prism, proving that the ray had been twisted round into 
a new position, in which its plane of polarisation was no 
longer at right angles to the plane of sjniimetry of the 
analyser. But if the analysing Nicol prism was itself 
turned round, a new position could, be found (at right 
angles to the plane of polarisation of the ray) at which 
the light was once more extinguished. The dii'ection oj 
the magneto-optic rotatio7i of the plane 0/ polarisation is 
the sa7ne (for diamag7ietic media) as that i7t ivhich the 
current flows which produces the magnetism. \^erdet, 
who repeated Faraday's experiments, using powerful 
electromagnets of the form shown in Fig. 127, dis- 
covered the important law that, with a given material, 
the amowit of rotation is proportional to the stf'ength oJ 
the magnetic fo7'ce H. In case the rays do not pass 
straight along the direction of the lines of force (which 
is the direction of maximum effect), the amount of rota- 
tion is proportional to the cosi7ie of the angle ^ between 
the directio7i of the ray a7id the lines offoixe. It is also 
proportional to the le7tgth I ^of the 77tate7'ial tlwottgh 
which the rays pass. These laws are combined in the 
equation for the rotation ^ ; 

^ = 7e/ • H • cos /3 • /, 
where w is a coefficient which represents the specific 
magnetic rotatory power of the given substance, and is 
known as '' Verde fs consfa7tt:' Now, H -cos Q is the 



35^ 



ELEMENTARY LESSONS ON [chap, ix. 



r^rd^ved part of the magnetic force in the direction ol 
the i^y ; and H • cos jS • / is the difference of magnetic 
potential^ Between the point A where the ray enters and 
B where it leaves the medium. Hence w, the coefficient 
of specific magnetic rotatory power, is found by divid- 
ing the observed angular rotation by the difference of 
magnetic potential between the points where the ray 
enters and leaves the mediunl ; or 

e 

Different substances possess different magnetic rotatory 
powers. For diamagnetic substances the coefficient is 
usually positive ; but in the case of many magnetic 
substances, such as solutions of ferric chloride, has a 
negative value ; {t,e. in these substances the rotation is 
in the opposite direction to that in which the magnetising 
current flows). The phenomenon discovered by Hall 
(Art. 337) appears to be intimately related to the 
phenomenon of magneto-optic rotation. 



Bisulphide of Carbon 
Water .... 
Heavy glass . 


Coefficient of Specific 
.. Magnetic Rotation, 
(Verdet's Constantino. G. S.) 


Magnetic 

Rotatory 

Power. 


1-5235 X 10-5 

•4693 X 10-5 

2-665 ^ ^^""^ 


i-ooo 

•308 
1-422 



It is convenient, for purposes of reference, to take the 
rotatory power of bisulphide of carbon as unity. Careful 
measurements executed by J. E. H. Gordon have shown 
that the rotatory power of bisulphide of carbon, thus 
assumed as a standard, must be multiplied by 1*5235 x 
io""5 to reduce it to C.G. S. measure ; for he finds that 

1 For /orce X length = work; and the work done in bringing a unit 
magnetic pole from A to B against the magnetic force lAeasures th? 
difference of magnetic potential. See Art. 310 (^). 



CHAP. IX.] ELECTRICITY AND MAGNETISM. 357 

this is the number of radians through which a polarised 
ray of green light (of thallium flame) will be rotated by 
traversing unit difference of potential. For rays of 
different colours the rotation is not equal, but varies 
(very nearly) inversely as the square of the waye-length ; 
the rotation by bisulphide of carbon of red, green, and 
blue light (rays "C," "E," and "G"), being respectively 
as -60, I -00, and i -65. H. Becquerel, who gave this law, 
also found that for substances of similar nature the rota- 
tion depends on the refractive index, but in rather a com- 
plicated relation, being proportional to ^2 (^2 — i) ; 
where fjj is the refractive index. 

Gases also rotate the plane of polarisation of light in 
a magnetic field with varjdng amounts; coal-gas 'and 
carbonic acid being more powerful than air or hydrogen ; 
oxygen and ozone being negative. The rotation is in all 
cases very slight, and varies for any gas in piopoition to 
the density — that is to the quantity of gas traversed. H. 
Becquerel has lately shown that the plane of the natural 
polarisation of the sky does not coincide with the plane 
of the sun, but is rotated by the influence of the earth's 
magnetism through an angle which, however, only reached 
59' of arc at a maximum on the magnetic meridian. 

388. Photo - magnetic Properties of Iron. — Dr. Kerr 
showed in 1877 that a ray of polarised light is also rotatied 
when reflect ed at the su7-face of a vjagvet or electromagnet. 
When the light is reflected at a pole the plane of polarisation is 
turned in a direction contrary to that in which the magnetising 
current flows. If the light is reflected at a point on the side of 
the magnet it is found that when the .plane of polarisation is 
parallel to the plane of incidence the rotation is in the same 
direction as that of the magnetising current ; but that, when the 
plane of polarisation is perpendicular to the plane of incidence, 
the rotation is in the same direction as that of the magnetising 
current only when the incidence exceeds 75°. 

Kundt showed in 1884 that a film of metallic iron so thin as 
to be transparent, placad across the lines of force of the magnetic 
field, rotates the plane of polarisaiion of transmitted light 
strongly in the direction in which the magnetising current flows. 



353 ELEMENTARY LESSONS ON [ciiAP. x:l 

389. Photo-voltaic Properties of Selenium. — 
In 1875 Willoughby Smith discovered that the metal 
selenmm possesses the abnormal property of changing 
its electric resistance under the influence of light. 
Ordinary fused or vitreous selenium is a very bad 
conductor; its resistance being nearly forty -thousand- 
million (3*8 X 10^^) times as great as that of copper. 
When carefully annealed (by keeping for some hours at 
a temperature of about 220°C5 just below its fusing 
point, and subsequent slow cooling), it assumes a crystal- 
line condition, in which its electric resistance is consider- 
ably reduced. In the latter condition, especially, it is 
sensitive to light. Prof. W. G. Adams found that green- 
ish-yellow rays were the most effective. He also showed 
that the cha7tge of electric resistance va7'ies directly as 
tlie square root of the ilhc77ii7iation^ and that the resist- 
ance is less with a ' high electromotive-force than a 
low one. Lately, Prof. Graham Bell and Mr. Sumner 
Tainter have devised forms of " selenium cells," in which 
the selenium is formed into narrow strips between the 
edges of broad conducting plates of brass, thus securing 
both a reduction of the transverse resistance and a large 
amount of surface-exposure to light. Thus a cell, whose 
resistance in the dark was 300 ohms, when exposed to 
sunlight had a resistance of but i 50 ohms. This pro- 
perty of selenium the latter experimenters have applied 
in the construction of the Photophone, an instrument 
which transmits sounds to a distance by means of a 
beam of light reflected to a distant spot from a thin 
mirror thrown into vibrations by the voice ; the beam 
falling, consequently, with varying intensity upon a re- 
ceiver of selenium connected in circuit with a small 
battery and a Bell telephone (Art. 435) in which the 
sounds are reproduced by the variations of the current- 
Similar properties are possessed, to a smaller degree, 
by telluriufn, Carbgn is also sensitive to light. 

About the middle of the 19th century Becquerei 
showed that when two plates of silver, coated with 



CHAP. IX.] ELECTRICITY AND MAGNETISM. 359 

freshly deposited chloride of silver, are placed in a cell 
with water and connected with a galvanometer, a current 
is observed to pass when light falls upon one of the two 
plates, the exposed plate acting as a negative pole. 

390. Electromagnetic Theory of Light. — Clerk. 
Maxwell proposed a theory of the relation betweerf 
electromagnetic phenomena and the phenomena of light, 
based upon the assumption that each of these are due to 
certain modes of motion in the all-pervading " cBther " of 
space, the phenomena of electric currents and magnets 
being due to streams and whirls, or other bodily move- 
ments in the substance of the aether, while light is due 
to vibrations to and fro in it. 

We have seen (Arts. 1 15, 338, and 387) what evidence there 
is for thinking that magnetism is a phenomenon of rotation, 
there being a rotation of something around an axis lying in the 
direction of the magnetisation. Such a theory would explain 
the rotation of the plane of polarisation of a ray passing through 
a magnetic field. For a ray of plane-polarised light may be con- 
ceived of as consisting of a pair of (oppositely) circularly-polarised 
waves, in which the right-handed rotation in one ray is periodi- 
cally counteracted by an equal left-handed rotation in the other 
ray ; and if such a motion were imparted to a medium ift which 
there were superposed a rotation (such as ^^e conceive to take 
place in every magnetic field) about the same direction, one of 
these circularly-polarised rays would be accelerated and the other 
retarded, so that, when they were again compounded into a 
single plane-polarised ray, this plane would not coincide with the 
original plane of polarisation, but would be apparently turned 
round through an angle proportional to the superposed rotation. 

It was 'pointed out (Art. 337) that an electric dis- 
placement produces a magnetic force at right angles to 
itself; it also produces (by the peculiar action known as 
induction) an electric force which is propagated at right 
angles both to the electric displacement and to the mag- 
netic force. Now it is known that in the propagation of 
light the actual displacements or vibrations which con- 
stitute the so-called ray of light are executed in directions 
at right angles to the direction of propagation. This 



360 



ELEMENTARY LESSONS ON [chap. ix. 



analogy is an important point in the theory, and 
immediately suggests the question whether the respective 
rates of propagation are the same. Now the velocity 
of propagation of- electromagnetic induction is that 
velocity "^" which was shown (Art. 365) to represent 
the ratio between the electrostatic and the electro- 
magnetic units, and which (in air) is believed to be 

2-9857 X 10^^ centimetres per second. 
And the velocity of light (in air) has been repeatedly 
measured (by Fizeau, Cornu, Michelson, and others) 
giving as the approximate value 

2*9992 X 10^^ centimetres per second. 
The close agreement of these figures is at least remarkable. 
Amongst other mathematical deductions from the theor)' may be 
mentioned the following : (i. ) all true conductors of electricity 
must be opaque ^ to light; (ii.) for transparent media the 
specific inductive capacity ought to be equal to the square ol 
the index of refraction. Experiments by Gordon, Boltzmann, 
and others, show this to be approximately true for waves of very 
great wave-length. The values are shown below. For gases 
the agreement is evtn closer. 



Flint Glass . 
Bisulphide of Carbon 
Sulphur (mean) 
Paraffin . 


K. 


f^'. 


3-162 

I'8l2 

4-151 
2-32 


2796 
2 -606 
4-024 
2-33 



1 The Author of these Lessons has found that in some crystalline bodies 
which conduct electricity better in one direction than in another, the opacity 
to light differs correspondingly. Coloured crystals of Totirmaline coudiict 
electricity better across the long axis of the crystal than along that axis. 
Such crystals are much more opaque to light passing along the axis than 
to light passing across it. And, in the case of rays traversing the crystal 
across the axis, the vibrations across the axis are more completely absorbed 
than those parallel to the axis : whence it follows that the transmitted li^ht 
will be polarized. 

Prof. H. Hertz has shown (i883) that invisible electric undulations ard 
propagated across space just as light-waves are ; for he ha3 been able to 
produce the phenomena of interference between two sets of them. 



CXiAP. X,] ELECTRICITY AND MACuN ETiSM. ^#i 



CHAPTER X. 

INDUCTION CURRENTS (Magneto-Electricity). 
Lesson XXXVl.-^Currenis produced by Induction. 

391. In 1831 Faraday discovered that currents can 
be induced in a closed circuit by moving magnets near 
it, or by moving the circuit across tJie magnetic field, 
and he followed up this discovery by finding that a 
current whose strength is changing may induce a 
secondary current in a closed circuit near it. Such 
currents, whether produced by magnets or by other 
currents, are known as Induction Oiui'ents. And 
the action of a magnet or current in producing such 
induced currents is termed electromagnetic induc- 
tion.i 

392. Induction Currents produced by a Magr- 
net. — If a coil of insulated wire be connected in circuit 
with a delicate (long-coil) galvanometer, and a magnet 
be inserted rapidly into the hollow of the coil (as in Fig. 

1 The student must not confuse this electromagnetic induction with the 
phenomenon of the electrostatic induction of one charge of electricity by 
another charge ^ as explained in Lesson III., and which has nothing to do 
with currents. Formerly, before the identity of the electricity derived from 
different sources was understood (Art. 318), electricity derived thus from the 
motion of magnets was termed magneto-electricity. For most purposes the 
adjectives magneto-electric and electro -magnetic rre synonymous. The 
production of electricity from magnetism, and of magnetism from electricity, 
are, it is true, two distinct operations ; but both are included in -the branch 
of science denominated Eleciroma^netics, 



3^- 



ELEMENTARY LESSONS ON [chap. x. 



146), a momentary current is observed to flow round 
the circuit while the magnet is being moved into the 
coil. So long as the magnet lies motionless in the coil 
it induces no currents. But if it be rapidly pulled out of 

the coil another momentary 
current will be observed to 
flow, and in the opposite direc- 
tion to the former. The in- 
duced current caused by in- 
serting the magnet is an 
inverse ctc7'rent^ or is in the 
opposite direction to that 
which would magnetise the 
magnet with its existing polar- 
ity. The induced current 
caused by withdrawing the 
magnet is a direct current. 

Precisely the same effect is 
produced if the coil be moved 
towards the magnet as if the 
magnet were moved toward 
the coil. The more rapid the motion is, the stronger 
are the induced currents. 

393. Induction Currents produced by Cur- 
rents. — Faraday also showed that the approach or 
recession of a current might induce a current in a closed 
circuit near it. This may be conveniently shown as an 
experiment by the apparatus of Fig. 147. 

A coil is joined up to a sensitive galvanometer as 
before. A smaller coil of stout wire is connected to the 
poles of a battery (a single Bunsen's cell in Fig. 147), so 
as to be traversed by a current. On approaching or 
inserting the smaller or "/r/;;/<^r/" coil into the larger 
or " secondary " coil, a momentary inverse current is 
produced ; and on removing it a momentary direct 
current (/.^., one which runs the same way round the 
outer secondary coil as the primary current which 




Fig. 146. 



CHAP. X.] ELECTRICITY AND MAGNETISM. 



3^3 



circulates in the inner coil) is observed. Breaking the 
battery circuit while the primary coil lies still within the 




iS 



secondary outer coil produces the same effect as if the 
primary coil were suddenly removed to an infinite dis- 
tance. Making the battery circuit while the primary 



3^4 



ELEMENTARY LESSONS ON [chap. x. 



coil lies within the secondary produces the same effect 
as plunging it suddenly into the coil. 

So long as a steady current traverses the primary 
circuit there are no induced currents in the secondary 
circuit, unless there is relative motion between the two 
circuits : but moving the secondary circuit towards the 
primary has just the same effect as moving the primary 
circuit towards the secondary, and vice versa. 

We may tabulate these results as follows : — 



By 

means 
of 


Momentary Inverse 

currents are induced 

in the secondary circuit 


Momentary Direct 

currents are induced 

in the secondary circuit 


Magnet 


while approaching. 


while receding. 


Current 


while approaching^ 

or beginnings 

or increasing in strength. 


while receding^ 

or ending^ 

or decreasing in strength. 



394. Fundamental Laws of Induction. — When 
we reflect that every circuit traversed by a current has a 
field of magnetic force of its own in which there are lines- 
of-force running through the circuit (Art. 192), and that a 
coil of many turns has a field in which the lines-of-force 
are distributed almost identically as those of a magnet 
are, we shall see that the facts tabulated in the preceding 
paragraph may be summed up in the following funda- 
mental laws : — 

(i.) A decrease in the number of lines-of-force which 
pass through a circuit produces a current round 
the ciraiit in the positive direction (/.^., produces 
a ^^ direct '^^ current^; while an increase in tJte 
nuwber of lines-offorce which pass through the 



CHAP. X.] ELECT:RICITY and magnetism. 365 

circuit produces a cun'ent In the negative direction 
round the cirom't. 

Here we suppose ^q positive direction along lines-of-force to 
be the direction along which a free N. -pole would tend to move, 
and positive direction round the circuit to be the same as the 
direction in which the hands of a clock move. {See also p. 275.) 

(ii.) The total induced electron Lotive'fo7'ce acting 
7'ound a closed circuit is equal to the rate oj 
decrease in the number of lines-of-force which 
pass th7^ough the circuit. 

Suppose at first the number of lines-of-force passing through 
the circuit to be N^, and that after a very short interval of time, 
/, they are Ng, then the total induced electiomotive -force E is 

^~ ~r~ • 

By Ohm's law, C = E -- R, therefore 

>-i _ Ni — Na 
^ - Rl • 
If Ng is greater than N^, and there is an increase in the number 
of line?-of-foice, then Nj •— Ng will be a negative quantity, and 
C will have a negative sign, showing that the current is an 
inverse one. 

A reference to Fig. 1 34 will make this important law clearer. 
Suppose A BCD to be a wire ciicuit of which the piece AB can 
slide along DA and CB towards S and T. Let the vertical 
arrows represent vertical' lines of force in a uniform magnetic 
field, and show (as is the case with the veitical components 
of the earth's lines-of-force in the northern -hemisphere) the 
diiection in which a N. -pointing pole would moveif fiee. The 
positive direction of these lines of force is theiefore veitical ly 
downwards through the circuit. Now if AB slide towards ST 
with a uniform velocity it will cut a certain number of lines-of- 
force every second, and a certain number will be added during 
every second of time to the total number passing through the 
circuit. If Ni be the number at the beginning, and Ng that at 
the end of a circuit, Nj — Ng will be a negative quantity, and 
there will be an electromotive -force round the circuit whose 
diiection through the sliding piece is from A towards B. 

395. The following adaptation of Ampere's rule to the case 
of induction may be useful ; Suppose a figure swimming in any 
condtutor to turn so cs io look along the {positive ditection of the) 



366 ELEMENTARY LESSONS ON [chap, x 

lines ^f -f or ce^ then if he and the conduccor be movc'd towards his 
right hand he will be swimming with the current induced by this 
motion ; if he be moved towards his left hand, the current will 
be against him. 

396. Lenz's Law. — In Art. 320 it was laid down that a 
circuit traversed by a current experiences a force tending to 
move it so as to include the greatest possible number of lines- 
of-force in the embrace of the circuit. ^ But if the number of 
lines -of-force be increased, during the increase there will be an 
opposing (or negative) electromotive - force set up, which will 
tend to stop the original current, and therefore tend to stop the 
motion. » If there be no current to begin with, the motion will 
generate one, which being in a negative direction will tend to 
diminish the number of lines - of - force passing through the 
circuit, and so stop the motion. Lenz, in 1834, summed up 
the matter by saying that in all cases of electro fnagnetic induction 
the induced currents have such a direction that their reaction 
tends to stop the motion which produces them. This is known 
as Lenz's Law. 

397. Mutual Induction of Two Circuits.— In 
Art. 3 20 it was shown that when two circuits, in which 
currents of unit strength are flowing, are placed near 
together, they have a mutual potential whose value we 
called M. This symbol M, upon investigation, was 
found to represent the number of lines -of- force which 
each circuit induced through the other circuit, or was 
" the number of each other's lines - of- force mutually 
intercepted by both circuits when each carries unit 
current." This number depended upon the form and 
position of the circuits, and was greatest when they 
were brought as near together as possible. Hence 
we may regard this quantity M as the^ " coefficient 
of mutual induction " of the two circuits ; and any 
movement of either circuit which alters the number 
of lines-of-force passing mutually through them, will 
be accompanied by the production of induced cur- 
rents in each. It can be shown mathematically that, 
in the case of two simple circular circuits of equal size, 
enclosing area S, the greatest number of lines-of-force 



CHAP. X.] ELECTRICITY AND MAGNETISM. 



367 



each can induce through the other, when each carries 
unit current, is 47rS. which is the maximum value of 
M. If the circuits are not simple, but have respectively 
in turns and n turns, then the value of M will be 
47rS X mn. when the circuits coincide with each other. 

398. The Induction Coil. — Induced currents have 
in general enomiously high electromotive-forces, and are 
able to spark across spaces that ordinary battery cur- 
rents cannot possibly cross. In order to observe these 
effects a piece of apparatus invented by Mason, and im- 
proved by Ruhmkorff, and termed the Induction Coil or 
Inductorium (Fig. 148), is used. The induction coil con- 
sists of a cylindrical bobbin having a central iron core 




surrounded by a short inner or " primary " coil of stout 
wire, and by an outer " secondary^' coil consisting of many 
thousand turns of very fine wire, very carefully insulated 
between its different parts. The primary circuit is joined 
to the terminals of a faw pov/erful Grove's or Bunsen's 
cells, and in it are also included an interruptor, and a 
commutator or key. The object of the interruptor is 



368 ELEMENTARY LESSONS ON [chap, x, 

to make and break the primary circuit in rapi<i sue- 
cession. The result of this is at every " make " to induce 
in the outer " secondary " circuit a momentary inverse 
current, and at every " break " a powerful momentary 
direct current. The currents at " make " are sup- 
pressed, as explained below : the currents at " break " 
manifest themselves as a brilliant torrent of sparks 
between the ends of the secondary wires when brought 
near enough together. The primary coil is made of 
stout wire, that it may carry strong currents, and produce 
a powerful magnetic field at the centre, and is made of 
few turns to keep the resistance low, and to avoid self- 
induction of the primary current on itself. The central 
iron core is for the purpose of increasing, by its great 
coefficient of magnetic induction, the number of lines- 
of- force that pass through the coils: it is usually made 
of a bundle of fine wires to avoid the induction currents, 
which if it were a solid bar would be set circulating in 
it, and which would retard its rapidity of magnetisation 
or demagnetisation. The secondary coil is made with 
many turns, in order that the coefficient of mutual 
induction may be large ; and as the electromotive-force 
of the induced currents will be thousands of volts, its 
resistance will be immaterial, and it may be made of the 
thinnest wire that can conveniently be wound. In Mr. 
Spottiswoode's giant Induction ^ Coil (which j^ields a 
spark of 42|- inches' length in air, when worked with 30 
Grove's cells), the secondary coil contains 280 miles of 
wire, wound in 340,000 turns, and has a resistance of 
over 100,000 ohms. 

TJie interruptors of induction coils are usually self- 
acting. That of Foucault, shown with the coil in Fig. 
148, consists of an arm of brass L, which dips a platinum 
wire into a cup of mercury M, from which it draws the 
point out, so breaking circuit, in consequence of its 
other end being attracted toward the core of the coil 
whenever it is magnetised ; the arm being drawn back 



CHAP. x.j| ELECTRICITY AND MAGNETISM. 369 

again by a spring when, on the breaking of the circuit, 
the core ceases to be a magnet. A more common 
intemiptor on small coils is a " break," consisting of a 
piece of thin steel which makes contact with a platinum 
point, and which is drawn back by the attraction of the 
core on the passing of a current ; and so makes and 
breaks circuit by vibrating backwards and forwards just 
as does the hammer of an ordinary electric bell 

Associated with the primary circuit of a coil is usually 
a small condenser^ made of alternate layers of tinfoil and 
paraffined paper, into which the current flows whenever 
circuit is broken. The object of the condenser is, firstly, 
to make the break of circuit more sudden by preventing 
the spark of the " extra- current " (due to self-induction 
in the primary circuit) (Art. 404) from leaping across 
the interruptor ; and, secondly, to store up the electricity 
of this self-induced extra-current at break for a brief 
histant, and then discharge it back through the primary 
coil so as to hasten demagnetisation and so augment 
the induced direct electromotive-force in the secondary 
coil. 

399. Rnhmkorff's Oommutator.— In order to 
cut off or reverse the direction of the battery current at 
will, Ruhmkorff invented the cormnutator or current- 
reverser, shown in Fig. 149. In this instrument the 
battery poles are connected through the ends of the 
axis of a small ivor)' or ebonite cylinder to two cheeks 
of brass V aad V, which can be turned so as to place 
them either way in contact with two vertical springs B 
and C, which are joined to the ends of the primary coil. 
Many other forms of commutator have been devised ; 
one, much used as a key for telegraphic signalling, is 
dra\yn in Fig. i 59. 

400. Luminous Bflfects of Induction Sparks.— 
The induction coil furnishes a rapid succession of sparks 
with which all the effects of disruptive discharge may be 
studied. These sparks differ only in degree from those 



370 



ELEMENTARY LESSONS ON [chap. x. 



furnished by friction machines .and by Leyden jars {see 
Lesson XXI I L on Phenomena of Discharge). 

V 




Fig. 149. 

For studying discharge through glass vessels and tubes 
from which the air has been partially exhausted, the 
coil is very useful Fig. 150 illustrates one of the 
many beautiful effects which can be obtained, the spark 
expanding in the rarefied gas into flickering sheets of 
light, exhibiting stri^ and other complicated phenomena. 

401. Currents Induced in Masses of Metal.— 
A magnet moved near a solid mass or plate of metal 
induces in it currents, which, in flowing through it frOiTi 
one point to another, have their energy eventually 
frittered down into heat, and which, whiie they last, 
produce (in accordance with Lenz'b law) electromagnetic 
forces tending to stop the motion. Several curious 
instances of this are known. Arago discovered that 
when a disc of copper is rotated in its own plane under 
a magnetic needle the needle turns round and follows 
the disc : and if a magnet is rotated beneath a balanced 
metal disc the disc follov/s the magnet. Attempts were 
made to account for these phenomena — known as 



CHAP. X.] ELECTRICITY AND MAGNETISM. 



i7i 



Arago^s rotations — by supposing there to be a sort of 
magnetism of rotation, until Faraday proved them to 
be due to induction. A 
magnetic needle set swing- 
ing on its pi^'ot comes to 
rest sooner if a copper disc 
lies beneath it, the induced 
currents stopping it. If a 
cube or disc of good con- 
ducting metal be set spin- 
ning between the poles of 
such an electromagnet as 
that drawn in Fig. 127, 
and the current be suddenly 
turned on, the spinning metal 
stops suddenly. If, by sheer 
force, a disc be kept spin- 
ning between the poles of 
a powerful electromagnet it 
will get hot in consequence 
of the induced currents flow- 
ing through it. In fact, 
any conductor nu)ved forc- 
ibly across the lines -of- 
foi'ce of a magnetic field 
experiences a mechanical 
resistance due to the in- 
duced currents which op- 
pose its motion. 

402. Induction - cin:- 
rents from Earth's Mag- 
netism. — It is easy to ob- 
tain induced currents from the earth's magnetism. A 
coil of fine wire joined to a longrcoil galvanometer, Avhen 
suddenly inverted, cuts the lines -of- force of the earth's 
magnetism, and is traversed accordingly by a current. 

Faraday, indeed, applied this method to investigate 




Fig. 150. 



372 ELEMENTARY LESSONS ON tCHAP. K. 

the dnrection and number of lines-of force. If a small 
wire coil be joined in circuit with a long coil galvan- 
ometer having a heavy needle, and the little coil be sud- 
denly inverted while in a magnetic field, it will cut all 
the lines-of-force that pass through its own area, and 
the sine of half the angle of the first swing (see Art. 
204) will be proportional to the number of lines of 
force cut ; for with a slow-moving needle, the total quan- 
tity of electricity that flows through the coils will be the 
integral whole of all the separate quantities conveyed 
by the induced currents, strong or weak, which flow 
round the circuit during the rapid process of cutting 
the lines-of-focce ; and the little coil acts therefore as a 
magnetic proof -plane. 

If the circuit be moved parallel to itself across a urii- 
form magnetic field there will be no inducfion currents, 
for just as many lines-of-force will be cut in moving 
ahead in front as are left behind. There will be no cur- 
rent in a wire moved parallel to itself along a line-of-force ; 
nor if it lie along such a line while a current is sent 
through it will it experience any mechanical force. 

403. Earth Ourrents. — The variations of the 
earth's magnetism, mentioned in Lesson XII., alter the 
number of lines-of-force which pass through the tele- 
graphic circuits, and hence induce in them disturbances 
which are known as " earth currents." During magnetic 
storms the earth currents on the British lines of telegraph 
have been known to attain a strength of 40 milli -amperes, 
which is stronger than the usjual working currents. 
Feeble earth currents are observed every day, and are 
more or less periodic in character. 

404. Self-induction: Extra Currents.— In Art. 
397 the induction of otie circuit upon another was ex- 
plained, and was shown to depend upon the numbef of 
lines-of-force due to one circuit which passed through 
the other, the coefficient 0/ mutual induction M being 
the number of mtitual lines-of-force embraced by both 



CHAP, x.l ^.LECTRICITY AND MAGNETISM. 373 

circuits when each carried unit current. Now, if two 
such circuits approach one another so as actually to 
coincide, the mutual induction becomes a. self-induc- 
tion of the circuit on itself. For every circuit there is a 
coefficieni of self-induction^ whose value depends upon the 
form of the circuit, and which will be greater if the 
circuit be coiled up into many turns, so that one loop of 
the circuit can induce lines-of-force through another loop 
of the same. Let L represent the coefficient of self-in- 
duction of one circuit, and L' that of a second circuit 
equal to the first. When these two circuits coincide with 
one another their coefficient of mutual induction (/.^., the 
num.ber of lines-of-force running through both circuits, 
each carrying unit current) M will be. equal to L + L'; 
or, L = J M. Now for two coincident circuits having 
n turns' each, and each of area S (by Art. 397), 
M = 47rS;^2. 

hence the coefficient of self-induction for one circuit 
of n turns coiled up in ane plane, 
L — 47rS;/2, 

The existence of self-induction in a circuit is attested by 
the so-called extra-onrrent, which makes its appear- 
ance as a bright spark at the moment of breaking circuit. 
If*rthe circuit be a simple one, and consist of a straight 
wire and a parallel return wire, there will be little or no 
self-induction; but-if the circuit be coiled up, especially if 
it be coiled round an iron bar, as in an electromagnet, 
then on breaking circuit there will be a brilliant spark, and 
a person holding the two ends of the wires between which 
the circuit is broken may. receive a slight shock, owing 
to the high electromotive-force of this self-induced extra 
current. The extra - current due to self-induction on 
"making" circuit is an inverse^ current, and gives no spark, 
but it prevents the battery current from rising at once to 
its full value. The extra-current on breaking circuit is 
a direct current, and therefore increases the strength of 
the current just at the moment when it ceases altogether 



374 ELEMENTARY LESSONS ON fcHAP. x. 

405. Helmholtz's Equation — Helmholtz, who investi- 
gated mathematically the effect of self-induction upon the strength 
of a current, deduced the following important equations to ex- 
press the relation between the self-induction of a circuit and the 
time required to establish the current at full strength : — 

The current of self-induction at any moment \\ill be propor- 
tional to the rate at which the current is increasing in strength. 
Let r represent a very short interval of time, and let the curient 
increase during that short interval from C to C +c. The actual 
increase during the interval is c, and the rate of increase in 

strength is -. Hence, if the coefficient of self-induction be L, 

the electromotive-force of self-induction will be - L-, and, if 
the whole resistance of the circuit be R, the strength of the 
opposing extra-current will be-W.- during the short interval 

T ; and hence the actual strength of current flo^^ ing in the 
circuit during that short interval instead of being (as by Ohm's 
Law it would be if the current were steady) C = E -r- R, will be 

P _ E _^ L £ 

^ - R R*r* 

To find out the strength at which the cunent will have arrive<l 
after a time / made up of a number of such small inter\als added 
together requires an application of the integral calculus, which 
at once gives the following result : — 



' = 10 -^"^'X 



(whero e is the base of tiie natural logarithms). 

Put into words, this expression amounts to saying that after 
a lapse of / seconds f/ie seJf-indifciion in a cu'aiit on making 
co7itact has the effect of diminishing the strength of the cw^reni by 
a quantit)^ the logarithm of whose reciprocal is inversely propor- 
tional to the coefficie7it of self induction^ and directly proportional 
to the resistance of the circuit and to the ti?ne that has elapsed 
si J tee makin.o circicit, 

A very brief consideration will show that in those cases where 
the circuit is so arranged that the coefficient of self-induction, 

L, is small as compared with the resistance R, the fraction £ 

Will have a high value, and the term ( -r^) will vanish from 
ihe equation for all appreciable values of /. 



CHAP. X.J ELECTRICITY AND MACxNETISM. 375 

Where, however, L is large as compared with R, as in long 
coils, long lines of telegraph cable, etc.. the value of this term, 
which stanvls for the refardation due to self-indiictioii^ may 
become considerable. 

406. Induced OTirrents of Higher Orders. — 
Professor Henry discovered that the variations in the 
strength of the secondary current could induce tertiary 
currents in a third closed circuit, and that variations in 
the tertiary currents might induce currents of a fourth 
order, and so on. A single sudden primar)" current pro- 
duces therefore two secondary currents (one inverse and 
one direct), each of these produces two tertiary currents, 
or four tertiary currents in all. But where the primary 
current simply varies in strength in a periodic rise and 
fall, — as when a musical note is transmitted by a micro- 
phone or telephone (Art. 435), — there will be the same 
number of secondary and tertiary fluctuations as of 
primary, each separate induction involving, however, a 
retardation of a quarter of the full period. 

406 [hi:). Transformers. — Of late years a new use has 
been found for induction-coils for the distribution of rapidly 
alternating currents (see Art. 411 ^) for electric lighting. Such 
induction-coils, known as transformers, usually consist of a 
core of thin jdates or Mdres of iron, interlaced with two sets of 
copper- wire coils, a primary consisthig of many turns of thin 
wire, to receive the incoming small currents at high potential, 
and a secondary consisting of a few turns of thick Avire, to deliver 
the large currents which go out at low potential to the lamps. 
The number of watts given out by the secondary is, in a well- 
constructed transformer, equal, within a ver)^ small percentage 
to the number of watts supplied to the primary coil ; ndiilst the 
volts of the secondary are to the volts at the prhiiary in pio- 
portion to the respective number of turns in the two coils. 

Lesson XXXVII. — Magneto-elecU-ic and Dynamo- 
electric Generators. 

407. Faraday's discovery of the inunction of currents 
in wires by moving them across a magnetic field sug- 
gested the construction of magneto-electric machines 



376 ELEMFNTARV LESSONS ON [chap. x. 

lo generate currents in piace of voltaic batteries. In 
the early attempts of Pixii (1833), Saxton, and Clarke, 
bobbins of insulated wiie were fixed to an axis and spun 
rapidly in front of the poles of strong steel magnets, 
but. since the currents thus generated were alternately 
inverse and direct currents^ a co7nmuhitor (which rotated 
with the coils) was fixed to the axis to turn the successive 
currents all into the same direction. The little magneto- 
electric machines, still sold by opticians, are on this 
principle. Holmes and Van Malderen constuicted moie 
powerful machines, the latter getting a neaier approach 
to a continuous current by combining around one axis 
sixty -four separate coils rotating between the poles ol 
forty powerful magnets. 

In 1856 Siemens devised an improved armature, in 
which the coils of wire were wound lejiglhways along 
a spindle of peculiar form, thereby gaining the advantage 
of being able to cut a greater number of Hues -of- force 
when rotated in the powerful "field" between the poles 
of a series of adjacent steel magnets. The next im- 
provement, due to Wilde, was the employment of elec- 
tromagnets instead of steel magnets for producing the 
" field " in which the armature re\ olved ; these electro- 
magnets being excited by currents furnished by a small 
auxiliary magneto-electric machine, also kept in rotation. 

408. Dynamo-electric Machines. — In 1867 the 
suggestion was made simultaneously, but independent!)', 
by Siemens and by Wheatstone, that a coil rotating 
between the poles of an electromagnet might from the 
feeble residual magnetism induce a small cuirent, which, 
when transmitted through the coils of the electromagnet, 
might exalt its magnetism, and so prepare it to induce 
still stronger currents. Magneto-electric machines con- 
structed on this principle, the coils of their field-magnets 
being placed in circuit with the coils of the iotating 
armature, so as to be tra\ersed by the whole or by a 
portion of the induced currents, are known as dynamo- 



CHAP. xO ELECTRICITY AND MAGNETISM. J77 

electric machines or generators, to distinguish them 
from the generators in which permanent steel magnets 
are employed. In either case the current is due to 
magneto-electric induction ; and in either case also the 
energy of the currents so induced is derived from the 
dynamical power of the steam-engine or other motor 
which performs the work of moving the rotating Coils 
of wire in the magnetic- field. Of the many modern 
machines on this principle the most famous are those of 
Siemens, Gramme, Brush, a^nd Edison. They differ 
chiefly in the means adopted for obtaining practical con- 
tinuity in the current. In all of them the electromotive- 
force generated is proportional to the number of turns 
of wire in the rotating armature, and (within certain 
limits) to the speed of revolution. When currents of 
small electromotive-force, but of considerable strength, 
are required, as for electroplating, the rotating armatures 
of a generator must be made with small internal resist- 
ance, and therefore of a few turns of stout wire or ribbon 
of sheet copper. For producing currents of high electro- 
motive-force for the purpose of electric lighting, the 
armature must be driven very fast, and must consist of 
many turns of wire, or, where ,very small resistahce js 
necessary (as in a system of lamps arranged in. parallel 
arc), of rods of copper suitably connected. 

There are several ways of arranging the coils upon the rotating 
armature, and the methods adopted may be classified as follows : — 

1. Drum Armatures, in which the coils are wound longitudinally upon, 

the surface of a cylinder or drum. Examples : the Siemens (Alteneck) 
and Edison machines. 

2. Ring Armatures, in which the coils are wound around a ring. Ex- 

amples : the Pacinotti, Gramme, Brush, Gulcher, and Biirgii) 
machines. 

3. Fole Armatures, in which the Coils are arranged radially with their 

poles pointing outwards. Example : Lontin machine. 

4. Disc Armatures, having coils arranged in or on a disc. Examples : 

Niaudet, Wallace, Hopkinson, and Gordon. In an early madiine by 
Faraday a simple copper disc rotating between the poles of a magnet 
generated a continuous current. 



37^ ELEinIENTARY LESSONS ON [chap. x. 



There are aiso several ways of arranging the coils of 
the field-magnets, giving rise to following classification: — 

1. Series- Dynamo^ wherein the coils of the field-magnets are in series 

with those of the armature and the external circuit. 

2. Shunt- Dynamoy in which the coils of the lield-magnets form «i shunt 

cr shunts to the main circuit : and being made of m.ny turris of 
thinner wire, draw off only a fraction of th^ whole curreiit. 

3. SePa7'ately-excited Dyna/fio: one in which the currents u&ed to excite 

the field-magnets are derived from a separate machine. 

4. Com/>07i?id-Vynaj;io : parth excited by shunt coils, partlj' by series 

coils. 
All these varieties have their appropriate uses according to th-^ conditions 
under which they are applied. 

409. Siemens* Machine. — The d>namo-electiic 
generator, invented by Siemens and Von Hefner Alteneck, 
usually called the Siemens' machinej is shown in Fig. 
151. Upon a stout frame are fixed four powerful flat 
electromagnets, the right pair having their N. -poles 
facing one another and united by arched pieces or 
cheeks of iion. The two S. -poles of the left pair are 
similaily united. In the space between the right and 
left cheeks, which is, theiefore, a very intense magnetic 
field, lies a horizontal axis, upon which rotates an 
armature consisting of fifty -six separate longitudinal 
coils, each end of each^ coil being connected with a 
copper bar forming one segment of the collector or 
commutator at the anterior end of the axis. This 
armature differs from the earlier simple longitudinal 
armature of Siemens only in the multiplication and 
arrangement of its parts, the di^ ision into so many paths 
giving a current which is practically continuous. The 
collector, made up, as said, of copper bars or segments 
fixed upon a cylinder of insulating rnaterial, may be 
regarded as a split-tube. The current cannot pass from 
one segment to the next without traversing one of 
the fifty-six coils of the armature ; and, as the end of 
one coil and the beginning of the next are both con- 
nected to the same commutator bar, there is a continuous 
communication round the whole armature. . Against the 



CHAP. X.] ELECTRICITY AND MAGNETISM. 



379 



commutator press a pair of metallic brushes or springs, 
as contact pieces, which touch opposite sides at points 




Fig, 151. 



above and below, and so lead away into the circuit the 
current generated in the coils of the rotating armature. 
Suppose the lines-of-force in the field to run from right 
to left,^ and the armature to rotate left-handedly, as seen 
in Fig. 151, then, by the rule given in Art. 395, in all 

1 Their direction is not exactly thus when the generator Is working, as 
the magnetic force due to the currents in the coils, which is nearly horizontal 
in direction, changes the resultant magnetic force to an oblique direction 
across the field. It is for this reason that the commutator ** brushes " have 
to be displaced with a certain angular" "lead." A similar displacement of 
the brushes occurs in the Gramme and all other dynamo-electric generators, 
the degree of displacement to get maximum strength of current varying with 
the resistances in the external circuit and with ^e work done by the current 



38o ELEMENTARY LESSONS ON [chap. X. 

— — — — . ^ if t 

the separate wires of the coils, moving upwards on the 
right, there will be currents induced in a direction from 
the back toward the front. In all the separate wires of 
the coijs moving, downwards on the left of the axis, the 
induced currents will be in a direction from the front 
toward the back. Hence, if the coils are joined as 
described to the commutator bars all the currents thus 
generated in one half of the coils wiU be flowing tnfo 
the external circuit at one of the commutator brushes ; 
and all the reverse currents of the other half of the coils 
will be flowing ouf of the other brush. The terminal 
screws connected by wires to the commutator brushes 
correspond to the -f and -- poles of a galvanic battery, 
the coils of the field -magnets being included in the 
external circuit. 

410. Gramme's Machine. — In 1864 Pacinotti in- 
vented a magneto-electric machine, its armature being a 
toothed ring of iron with coils wound between the pro- 
jections. In 1870 Gramme invented a dynamo-electric 
machine having a ring armature differing only in being 
completely overwound with coils of insulated copper 
wires. The principle of this generator is shown in 
diagram in Fig. 152. The ring itself, made of a bundle 
of annealed iron wires, is wound in separate sections, 
the ends of each coil being joined to strips of copper 
which are insulated from each other,, and fixed sym- 
metrically as a commutator around the axis^ like a split 
tube. Their actual arrangement is shown again in Fig. 
153. The coils of the separate sections of the ring are 
connected together in series, each strip of the commu- 
tator being united to one end of each of two adjacent 
coils. Against the split -tube collector press metallic 
brushes to receive the current. When this ring is rotated 
the action is as follows : — Suppose (in Fig. 1 52) the ring 
to rotate in the opposite direction to the hands of a clock 
in. the magnetic field between the N and S-poles of a 
ma^rnet (or electro-magnet), and that the positive direc- 



CHAP. X.] ELECTRICITY AND MAGNETISM. 381 



tion of the lines of force is from N to S. As a matter 
of fact the lines will not be straight across from N to S, 
because the greater part of them will pass into the ring 
near N and traverse the iron of the ring to near S, where 
they emerge ; the space within the ring being almost 
entirely destitute of them. Consider one single coil of 
the wire wrapped round the ring at E" which is ascending 




Fig. 152. 

toward S ; the greatest number of lines-of- force will pass 
through its plane when it lies near E'', at right angles to 
the line NS. As it rises toward S and comes to E the 
number of lines-of-force that traverse it will be steadily 
diminishing, and will reach zero when it comes close to 
S and lies in the line NS, edgeways to the lines-of-force. 
As it moves on toward E' it will again enclose lines-of- 
force, which will, however, pass in the negative direction 
through its plane, and at E' the number of such negative 
lines-of-force becomes a maximum. Hence, through all 
its journey from E" to E' the nimiber of (positive) lines- 
of-force embraced by a strand of the coils has been 
diminishing ; during its journey round the other half from 
E' to E'' again, the number will be increasing. There- 
fore, by the rule given in Art. 395, in all the coils moving 
round the upper half of the ring direcf currents are being 



382 



ELEMENTARY LESSONS ON [chap. x. 



generated, while in the cons of the lower han of the ring 
inverse currents are being generated. Hence there is a 
constant tendency for electricity to flow from the left side 
at E' both ways round towards the right side at Y!\ and 
E"' will be at a higher potential than E'. A continuous 




Fig. 153. 

current will therefore be generated in an external wire, 
making contact at F and F by means of brushes, for as 
each successive coil moves up towards the brushes the 
induced current in it increases in strength, because the 
coils on eac.h side of this position are sending their 
induced currents also toward that point. Fig. 153 shows 
the little Gramme machine, 2 1 inches high, suitable for 



CHAP. X.] ELECTRICITY AND MAGNETISM. 383 

producing an electric arc light when driven by a 2| 
horse-power engine. Above and below are opposite 
pairs of powerful electro-magnets, whose iron pole-pieces 
project forwards and almost embrace the central ring - 
armature, which, with the commutator, is fixed to the 
horizontal spindle. 

411. {a) Brush's Machine. — In Brush's dynamo-eledtric 
generator, a ring-armature is also used, identical in form with 
that invented by Pacinotti, the iron ring being enlarged with 
protruding cheeks, with spaces between, in which the coils are 
wound, the coils themselves being also somewhat differently 
joined, each coil being united with that diametrically opposite 
to it, and having for the pair a commutator consisting of a collar 
slit into two parts. For each pair of coils there is a similar 
collar, the separate collars being grouped together and com- 
municating to two or more pairs of brushes that rub against them 
the currents which they collect in rotating. The electromotive- 
force of these machines is very high, hence they are able to 
drive a current through a long row of arc lamps connected in 
one series. The largest Brush machines capable of maintaining 
65 arc lights have an electromotive-force exceeding 3000 volts. 
In Giilcher's and Schuckert's machines the ring-armature takes 
the form of a flattened disk. In Crompton's dynamo the 
armature is wound on a hollow cylindiical core built up of flat 
thin iron rings. 

Siemens and others have devised another class of dynamo- 
electric machines, differing entirely from any of the preceding, 
in which a coil or other movable conductor slides round one 
pole of a magnet and cuts the lines of force in a continuous 
manner without any reversals in the direction of the induced 
currents. vSuch machines, sometimes called *' uni-polar '* 
machines, have, however, very low electromotive-force. 

411. {d) Edison's Machine. —Some very large dynamo- 
electric generators have been constructed by Edison for his 
system of electric lighting. This machine (as shown in Fig. 
154) is built upon the same bed-plate as the steam engine (of 
120 H-P) which drives it, and is called by its designer the 
stea))i-dyna}}io. The field-magnets are placed horizontally, and 
consist of 1 2 cylindrical iron bars overwound with wire, united to 
solid-iron pole-pieces weighing many tons. Between the upper 
and lower pole-pieces rotates the armature, which is a modifica- 
tion of the dmm- armature of Siemens, and is made up of 9S 



ELEMENTARY LESSONS ON [chap. x. 




CHAP. X.] ELECTRICITY AND MAGNETISM. 385 

long rods of copper connected by copper discs at the ends instead 
of coils of wire. The commutator or collector consists of 49 
parallel bars of copper, like the split-tube commutator of the 
other machines. The circuit of the armature runs from one bar 
of the commutator along one of the copper rods into a coppei 
disc at the far end, crosses by this disc to the opposite rod, 
along which it comes back to the front end to another copper 
disc connected to the next bar of the commutator, and so on all 
round. This arrangement greatly reduces the wasteful resistance 
of the armature, and adds to the efficiency of the machine. The 
interior of the armature is made up of thin discs of iron strung 
upon the axis to intensify the magnetic action while avoiding 
the currents which would be generated wastefully (see Art. 401) 
in the mass of the metal were the iron core solid. There are 
also S pairs of brushes at the commutator to diminish sparking. 
This machine has ,a very high efficiency, and turns 90 per cent 
of the mechanical power into electrical power. It is capable of 
maintaining 1300 of Edison's incandescent lamps (Art. 374) 
alight at one time. When driven at 300 revolutions per minute 
the current generated is about 900 amoeres, and the electio- 
motive^force 105 volts. 

411. (c) Theory of Continuous-Current Dynamo. — TJie 
electromotive -force of a dynamo depends (/) on the number 
of magnetic lines N which the field -magnet forces through the 
armature core, passing into it from the north -pole of the field- 
magnet on one side, and out of it into the south-pole of the 
field-magnet on the other ; (z'z) on the number of conducting 
wires or bars wound upon the armature ; (ni) on the speed of 
rotation. If we use the symbol C for the number of armature 
conductors counted all round the periphery, and n for the 
number of revolutions per second, then the electromotive-force 
of the dynamo (in absolute units) will be given by the rule 

E = wCN ; 
but since one volt is taken as 10^ absolute C.G.S. units (see 
Art. 323), the electromotive-force as expressed in volts will be 

E (volts) = ;^CN-^ lo^ 
The number I»^ of magnetic lines through the armature can be 
calculated by the rule for the magnetic circuit, given on p. 297, 
proper allowance being made for inevitable leakage of some of 
the magnetic lines. 

All and any of the contmuous-current magneto-electric and 
dynamo-electric machines can be used as electromotors, the 



386 ELEMENTARY LESSONS ON [chap, x. 



armature rotating and exerting power when a current from an 
independent source is led into the machine. 

411. (cf) Alternate -Current Machines. — In some dynamo- 
electric machines the alternately-directed currents generated by 
the successive approach and recession of the coils to and from 
the fixed magnet-poles are never commuted, but pass direct to 
the circuit. In a typical machine of this class invented by 
Wilde, the armature consists of a series of bobbins arranged 
upon the periphery of a disk which rotates between two sets of 
fixed electromagnets arranged upon circular frames, and pre- 
senting N and S- poles alternately inward. The alternate- 
current machine of Siemens is similar in design. Such 
machines cannot excite their own field-magnets with a constant 
polarity, and require a small auxiliary direct -current dynamo to 
excite their magnets. In another machine, devised by De 
Meritens, a ring -armature, resembling those of Pacinotti and 
Brush, moves in front'" of permanent steel magnets. In this 
machine the current induced in the circuit in one direction 
while the coils approach one set of poles is immediately followed 
by a current in the other direction as the coils recede from this 
set of poles and approach the set of poles of contrary sign. 
Alternate-current machines have also been devised by Lontin, 
Gramme, and others, for use in particular systems of electric 
lighting; as, for example, the JablochkofF candle (Art. 374). 
In Lontin's machine, as in the more recent and much largei 
disk- dynamo of Gordon, the field-magnet coils rotate between 
two great rings of fixed coils in which the currents are in- 
duced. A recent form of alternate-current machine, designed 
by Ferranti, differs from the machines of Wilde and Siemens in 
the substitution of copper strips wound in zig-zag, for the set 
of rotating bobbins in the armature. In ^lordey's alternator 
the field-magnet which rotates presents two crowns of opposing 
poles on either side of a stationary armature. 

411. (<?) Compound -Wound Machines. — The field-mag- 
nets of a dynamo- electric machine are sometimes wound with 
two sets of coils, so that it can be used as a combined shunt- 
and-series machine (see Art. 408). Such machines, when run 
at a certain "critical" speed, may be made to yield their 
current, at a constant electromotive- force whatever the resistances 
in circuit. 



CHAP. xi.J ELECTRICITY AND MAGNETISM. 387 



CHAPTER XL 

Electro-Chemistry. 
Lesson XXXVI I L — Electrolysis and Electrometallurgy. 

412. In Lessons XIV. and XVI 1 1, it was explained 
that a definite amount of chemical action in a cell 
evolves a current and transfers a certain quantity of 
electricity through the circuit, and that, conversely, a 
definite quantity of electricity, in passing through an 
electrolytic cell, will perform there a definite amount of 
chemical work. The relation between the current and 
the chemical work performed by it is laid down in the 
following paragraphs. 

413. Electromotive - force of Polarisation. — 
Whenever an electrolyte is decomposed by a current^ 
the resolved ions have a tendency to reunite, that 
tendency being commonly termed "chemical affinity," 
Thus, when zinc sulphate (Zn SO^) is split up into Zn 
and soothe zinc tends to dissolve again into the solution 
by reason of its "affinity" for oxygen and for sulphuric 
acid. But zinc dissolving into sulphuric acid sets up an 
electromotive-force of definite amount ; and to tear the 
zinc^ away from the sulphuric acid requires an .electro- 
niotive-force ^t least as great as this, and in an opposite 
direction to it. So, again, when acidulated water is 
decomposed in a voltameter, the separated* hydrogen 



388 ELEMENTARY LESSONS ON tcHAP. xi. 

and oxygen tend to reunite and set up an opposing 
electromotive -force of no less than 1*47 volts. This 
opposing electromotive-force, which is in fact the measure 
of their " chemical affinity," is termed the electrontotive- 
force of polarisation. It can be observed in any water- 
voltameter (Art. 208) by simply disconnecting the 
wires from the battery and joining them to a galvan- 
ometer, when a current will he observed flowing back 
through the voltameter from the hydrogen electrode 
toward , the oxygen electrode. The polarisation in a 
voltaic cell (Art. 163) produces an opposing electro- 
motive-force in a perfectly similar way. 

Now, since the affinity of hydrogen for oxygen is 
represented by an electromotive-force of 1*47 volts, it is 
clear that no cell or battery can decompose water unless 
it has an electromotive -force at least of 1*47 volts. 
With every electrolyte there is a similar minimum 
electromotive-force necessary to produce complete con- 
tinuous decomposition. 

414. Theory of Electrolysis. — Suppose a current 
to convey a quantity of electricity Q through a circuit 
in which there is an opposing electromotive -force E : 
the work done in moving Q units of electricity against 
this electromotive-force will be equal to E x Q. (If E 
and Q are expressed in "absolute" C.G.S. imits, E-Q 
will be in ergs.) The total energy of the current, * as 
available for producing heat or mechanical motion, will 
be diminished by this quantity, which represents the 
work done against the electromotive-force in question. 

But we can arrive in another way at an expression 
for this same quantity of work. For the quantity of 
electricity in passing through the cell will deposit a 
certain amount of metal : this amount of metal could be 
burned, or dissolved again in acid, giving up its potential 
energy as heat, and, the mechanical equivalent of heat 
being known, the equivalent quantity of work can be 
caleulatedT Q units of electricity will cause the depo* 



CHAP. XL] ELECTRICITY AND MAGNETISM. 389 



sition of Q2 grammes of an ion whose absolute electro- 
chemical equivalent is z. [For example, 2 for hydrogen is 
•00010352 gramme, being ten times the amount (see table 
in Art. 212) deposited by one coulomb, for the coulomb 
is iV of the absolute C.G.S. unit of quantity.] If H 
represent the number of heat units evolved by one 
gramme of the substance, when it enters into the com- 
bination in question, then Q^H represents the value (in 
heat units) of the chemical work done by the flow of the 
Q units ; and this value can immediately be translated 
into ergs of work by multiplying by Joule's equivalent J 
( = 42 X 10 6). [See Table on page 400.] 
We have therefore the following equality :— 
EQ = Q^HJ ; whence it follows that 
E = zYi] ; or, in words, the electromotive- 
force of any chemical reaction is equal to the product 0/ 
the electrO'Chemical equivalent of the separated ion into 
its heat of combination^ expressed in dynamical units. 

Examples. — (i) Electromotive -force of Hydrogen tending to 
unite with Oxygen, For Hydrogen z = '00010352 ; H 
(heat of combination of one gramme) = 34,000 gramme- 
degree-units ; J = 42 X 10^. 

•00010352 X 34,000 X 42 X 10^ = 1*47 X lo^ ** absolute" 
units of electromotive-force, or = 1*47 volts, 

(2) Electromotive force of Zirg dissolving into Sulphuric Acid, 

z = '003364 ; H = 1670 (according to Julius Thomsen) ,• 
J = 42 X 10^. 

•003364 X 1670 X 42 X 10® = 2*359 X 108. 
or = 2*359 volts, 

(3) Electromotive force ^Copper dissolving into Sulphuric Acid, 

z = -003261 ; H = 909*5 ; J = 42 X 106. 
•003261 X 909*5 X 42 X 10^ = 1*252 X 108. 
or = I '252 volts. 

(4) Electronwtive force of a Darnell's Cell. Here zinc is dissolved 

at one pole to form zinc sulphate, the chem-ical action setting 
up a 4- electrcniotive-fbrce, while at the other pole copper 
is deposited by the current out of a solution of copper 
sulphate, thereby setting up an opposing (or -) electro- 



390 



ELEMENTARY LESSONS ON [chap. xi. 



motive - force. That due to zinc is shown above to be 
+ 2*359 vvltSy that to deposited copper to' be - 1*242. 
Hence the net electromotive-force of the cejl is (neglecting 
the slight eledtromotive - force where the' two solutions 
touch) 2*359 - 1-242 = I •117 volts. This is nearly what 
is found (Art. 170) in practice to be the case. It is less 
than will suf&ce to electrolyse water, thoifgh two Daniell's 
cells in series electrolyse water easily. 

415. Secondary Batteries : Storage of Electric Currents. 
. — A voltameter, or series of voltameters, whose electrodes are 
thus charged respectively with hy- 
drogen and oxygen, will serve as 
secondary batteries^ in which the 
energy of a current may be stored up 
(as chemical work) and again given 
out. Ritter, who in 1803 con- 
structed a secondary pile, used elec- 
trodes of platinum. Gaston Plant^ 
in i860, devised a secondary cell 
consisting of two pieces of sheet 
lead rolled up (without actual con- 
tact) as electrodes, dipping into 
dilute sulphuric acid, as in. Fig. 
15s; the lead becoming with re- 
peated charges in alternate directions 
coated with a semi -porous film of 
brown dioxide of lead on the. anode 
plate, and on the kathode plate 
assuming ^ spongy metallic, state 
presenting a large amount of surface 
of high chemical activity. When 
such a battery, or accumulator of 
currents,^ is charged by connecting it 
with a dynamo- electric machine or 
other powerful generator of currents, 
the anode plate becomes peroxidis^d, 
while the kathode plate is deoxidised by the hydrogen that 
is liberated. The plates may remain for many days in this 
condition, and will furnish a current until the two lead surfaces 
are reduced to a chemically inactive state. The electro- 
motive-force of such cells is about 2'0 volts during discharge. 
Plante has ingeniously arranged batteries of such cells so that 
they can be charged in parallel arc, and discharged in series. 




Fig. 155- 



GHAP. XL] ELECTRICITY AND MAGNETISM. 



391 



giving (for a short time) currents of extraordinary strength. 
Eaure, in 1 88 1, improved the Plante accumulator by giving the 
two lead plates a preliminary coating of redhead (or minium). 
,When a current is passed through the cdll 'to charge it, the red- 
lead is peroxidised at the anode, and reduced, — first to a con- 
dition of lower oxide, then to the spongy metallic state, — at the 
kathode, and thus a greater thickness of the working substance 
is provided, and takes fair less time to form than is the case in 
Planters cells. For electric lighting, Faure's cells are made up 




Fig. 156. 

with flat plates in the form shown in Fig. 156. In Sellon's 
and Volckmar's accumulators the minium is packed into inter- 
stices in the lead plates. A secondary cell resembles a Leyden 
jar in that it can be charged and then discharged. Its time- 
rate of leakage is also similar. The residual charges of Leyden 
jars, though small in quantity and transient in their discharge, 
yet exactly resemble the polarisation charges of voltameters. 

416 Grove's Gas Battery.— Sir W. Grove devised a cell 
in which platinum electrodes^ in contact respectively with hy- 
drogen and oxygen gas, replaced the usual zinc and copper plates. 
Each of these gases is partially occluded by the metal platinum, 
which, when so treated, behaves like a different metal. In Fig. 
157 one form of Grove's Gas Battery is shown, the tubes O 
and H containing the + and - electrodes, surrounded with 
oxygen and hydrogen respectiveljf^ 



392 



ELEMENTARY LESSONS ON [chap. xi. 



417. General Laws of Electrolsrtic Action. — In 

addition to Faraday's quantitative laws given in Art. 211, 

the following are 
inii)ortant : — 

{(!,) Every 
electrolyte is de- 
composed into 
two portions, an 
anion and a ka- 
tion, which may 
be themselves 
either simple or 
compound. In 
the case of simple 
binary com- 
pounds, such as 
ifused salt (Na 
CI), the ions are 
simple elements. 
In other cases 
the products are 
often complicat- 
ed by secondary'' 
actions. It is 
even possible to 
deposit an alloy 
of two metals — 
^;*<i;i"y for example 
— fiom a mix- 
ture of the cya- 
nides of zinc and 
of copper. 
(?.) In binary l:ompounds and most metallic solutions, 

the metal is deposited by the current where it leaves the 

cell, at the kathode. 

((T.) Aqueous solutions of salts of the metals of the 

alkalies and alkaline earths deposit no metal, but evolve 




Fig. IS7- 



CHAP. XL] ELECTRICITY AND MAGNETISM. 393 

hydrogen owing to Secondary action of the metal upon 
the water. From strong solutions of caustic potash and 
soda Davy succeeded in obtaining metallic sodium and 
potassium, which were before unknown. If electrodes of 
mercury are employed, an amalgam of either of these 
metals is readily obtained at the kathode. The so- 
called ammomum^B.mBlgdim is obtained by electrolysing a 
warm, strong solution of salammoniac between mercury 
electrodes. 

(d:) Substances can be arranged in a definite series 
according to their electrolytic behaviour ; each substance 
on the list behaving as a kathion (or being " electroposi- 
tive ") when electrolysed from its compound with- any 
other on the list. In such a series the oxidisable metals/ 
potassium, sodium, zinc, etc., head the list ; after whith 
come the less oxidisable or "electronegative" metals J then 
carbon, oxygen, phosphorus, iodine, chlorine, sulphur, 
and lastly ozone. 

(e.) From a solution of mixed metallic salts the least 
electropositive metal is deposited first, unless the current 
be very strong. 

(/) The liberated ions appear only at the elec- 
trodes. 

{g.) For .each electrolyte a 7mmmum electromotive'" 
force is requisite, without which complete electrolysis 
cannot be effected. (See Art. 41 3-) 

(A.) If the current be of less electromotive-force than 
the requisite minimum, electrolysis may begin, and a 
feeble current flow at first, but no ions will be liberated, 
the current being completely stopped as soon as the 
opposing electromotive-force of polarisation has risen to 
equality with that of the electrolysing current. 

(/.) There is no opposing electromotive-force of polar- 
isation when electrolysis is effected^rom an anode of the 
same metal that is being deposited at the kathode. The 
feeblest cell will suffice to deposit copper from sulphate of 
copper if the anode be a copper plate. 

3 P 



394 ELEMEI^rrARY LESSONS ON Ichap. xi. 

(/.) Where the ions are gases, pressure affects the 
conditions but slightly. Under 300 atmospheres acid- 
ulated water is still electrolysed ; but in certain cases 
a layer of acid so dense as not to conduct collects at 
the anode and Stops the current. 

{^.) The che.mical work done by a current in an 
electrolytic cell is proportional to the minimum electro- 
inotive-force of polarisation. 

(/.) Although the electromotive-force of polarisation 
may exceed this minimum, the work done by the current 
in overcoming this surplus electromotive-force will not 
appear as chemical work, for no more of the ion will be 
liberated ; but it will appear as an additional quantity of 
heat (or *' local heat'') developed in the electrolytic cell. 
(m.) Ohm's law holds good for electrolytic conduction. 
(;/.) Amongst the secondarj^ actions which may occui* 
the following are the chief: — (i.) The ions may them- 
selves decompose ; as SO4 into SO3 + O. (2.) The ions 
may react on the electrodes ; as v/hen acidulated water 
is electrolysed between zinc electrodes, no oxygen being 
liberated, owing to the affinity of zinc for oxygen. (3.) 
The ions may be liberated in an abnormal state. Thus 
oxygen is frequently liberated in its allotropic condition 
as ozone, particularly when permanganates are electro- 
lysed. The " nascent " hydrogen liberated by the elec- 
trolysis of dilute acid has peculiarly active chemical 
properties. So also the metals are sometimes deposited 
abnormally : copper in a black pulverulent film ; anti- 
mony in roundish gray masses (from the terchloride 
solution) which possess a curious explosive property, etc. 
418. Hypotheses of Grotthuss and of Olaii* 
sius. — A complete theory of electrolysis must explain— 
firs^/y^ the transfer of electricity, and, secondly^ the transfer 
of matter, through the liquid of the cell. Tne latter 
point is the one to which most attention has bGen 
given, since the " migration of the ions " {i.e. their trans- 
fer through the liquid) in two opposite directions, aisd 



CHAP. XI.] ELECTRICITY AND MAGNETISM. 



395 



their appearance at the electrodes 07ily^ are salient 
facts. 

The hypothesis put forward in 1805 by Grotthuss 
serves fairly, when stated in accordance with modern 
terms, to explain these facts. Grotthuss supposes that, 
when two metal plates at different potentials are placed 
in a cell, the first effect produced in the liquid is that 
the molecules of the liquid arrange themselves in in- 
numerable chains, in which every molecule has its 
constituent atoms pointing in a certain direction ; the 
atom of electropositive substance being attracted toward 
the kathode, and the fellow atom of electronegative 
substance being attracted toward the anode. (This 
assumes the constituent atoms grouped in the molecule 
to retain their individual electric properties.) The 
diagram of Fig. 1 58 shows, in the case of Hydrochloric 




Fig. 158. 

Acid, a row of molecules i, i, at first distributed at 
random, and secondly (as at 2, 2,) grouped in a chain 
as described. The action which Grotthuss then sup- 
poses to take place is that an interchange of partners 
goes on between the separate atoms all along the line, 



39^ ELEMENTARY LESSONS ON [chap, xl 

each H atom uniting with the CI atom belonging to the 
neighbouring molecule, a + half molecule of hydrogen 
being liberated at the kathode, and a — half molecule 
of chlorine at the anode. This action would leave the 
molecules as in 3, 3, and would, v/hen repeated, result 
in a double migration of hydrogen atoms in one direc- 
tion and of chlorine atoms in the other, the free atoms 
appearing only at the electrodes, and every atom so 
liberated discharging a certain definite minute charge of 
electricity upon the electrode where it was hberated.^ 

Clausius has sought to bring the ideas of Grotthuss 
into conformity with the modem kinetic hypothesis of 
the constitution of liquids. Accordingly, we are to 
suppose that in the usual state of a liquid the molecules 
are always in movement, gliding about amongst one 
another, and their constituent atoms are also in move- 
ment, and are continually separating and recombining 
into similar groups, their movements taking place in all 
possible directions throughout the liquid. But under 
the influence of an electromotive-force these actions are 
controlled in direction^ so that when, in the course of the 
usual movements, an atom separates from a group it 
tends to move either toward the anode or kathode \ 
and if the electromotive force in question be powerful 
enough to prevent recombination, these atoms will be 
permanently separated, and will accumulate around the 
electrodes. This theory has the advantage of account- 
ing for a fact easily observed, that an electromotive force 
less than the minimum, which is needed to effect com- 
plete electrolysis may send a feeble current through an 

1 LIr. G. J. Stoney has lately reckoned, fron5 consi derations founded on 
the size of atoms (as calculated by Loschmidt dnd Sir V/. Thomson), that 
for every chemical bond ruptured, a char^^e of lo—^o of a coulomb is trans- 
ferred. [E. Budde s^ys 17 X lo--^ coulomb.] This quantity would appear 
therefore to be the natural atomic charc^e or unit. To tear one atom of 
hydrogen from a hydro|;en compound this amount of clectricicy must be senf 
through it. To liberate an atom of zinc, cr any other di-valent metal from 
its compound, implies the transfer of twice tliis amount of electricity. 



CHAP. XI.] ELECTRICITY AND MAGNETISM. 397 

electrolyte for a limited time, until the opposing electro- 
motive force has reached an equal value. Helmholtz, 
who has given the name of electrolytic convection to this 
phenomenon of partial electarolysis, assumes that it takes 
place by the agency of uncombined atoms previously 
existing in the liquid. This assumption is virtually in- 
cluded in the kinetic hypothesis of Clausius. 

419.' Electrometallurgy. — The applications of elec- 
tro-chemistry to the industries are threefold. Firstly^ 
to the reduction of metals from solutions of their ores, 
a process too costly for general application, but one 
useful in the accurate assay of certain ores, as, for 
example, of copper ; secondly^ to the copying of types, 
plaster casts, and metal -work by kathode deposits of 
metal ; thirdly^ to the covering of objects made of baser 
metal with a thin film, of another metal. Such as gold, 
silver, or nickel. All these operations arer included 
under the v general term of electro?netallw'gy. 

420. Electrotyping. ^ — In 1836 De La Rue ob- 
served-that in a Daniell's cell the copper deposited out 
of the solution upon the copper plate which served as a 
pole took the exact impress of the plate, even to the 
scratches upon it. In 1839 Jacobi in St. Petersburg, 
Spencer in Liverpool, and Jordan in London, independ- 
ently developed, out of this feet a method, of obtainmg, 
by the electrolysis of CQpp.er, impressions (in reversed 
relief) of coins, stereotype plates, and ornaments. A 
further improvement, due to Murray, was the employment 
of moulds of plaster or wax. coated with a film of pltim- 
ba^o in order to provide a conducting surface upon 
which the deposit could be made. Jacobi gave to the 
process the name of galvauo-pJastic^ a term generally 
abandoned in favour of the term eleotrotyping or 
electrotype process. 

Electrot}T)es of copper are easily made by' hanging a 
suitable mould in cell containing a saturated solution of 
sulphate of copper, and passing a current of a battery 



398 ELEMENTARY LESSONS ON [chap, xi 

through the cell, the mould being the kathode ; a plate 
of copper being employed as an anode, dissolving gradu- 
ally into the liquid at a rate exactly equal to the rate of 
deposition at the kathode. This use of a separate 
battery is more convenient than producing the electro- 
types in the actual cell of a DanielPs battery. The 
process is largely employed at the present day to repro- 
duce repouss^ and chased ornament and other works of 
art in facsimile, and to multiply copies of wood blocks 
for printing. Almost all the illustrations in this book, 
for example, are printed from electrotype copies, and not • 
from the original wood blocks, which Vw^ould not wear so 
well. 

421. Electroplating.— In 1801 WoUaston observed 
that a piece of silver, connected with a more positive 
metal, became coated with copper when put into a 
solution of copper. In 1805 Brugnatelli gilded two 
silver medals by making them the kathodes of a cell 
containing a solution of gold. Messrs. Elkington, about 
the year 1840, introduced the commercial processes of 
electroplating. In these processes a baser m^etal, such 
as German silver (an alloy of zinc, copper, and nickel) 
is covered with a thin film of silver or gold, the solutions 
employed being, for electro -gildings the double cyanide 
of gold and potassium, and for electro -silvering the 
double cyanide of silver and potassium. 

Fig« 159 shows a battery and a plating-vat containing 
the silver solution. From the anode is hung a plate of 
metallic silver which dissolves into the liquid. To the 
kathode are suspended the spoons, forks, or other 
articles which are to receive a coating of silver. The 
addition of a minute trace of bisulphide of carbon to the 
solution causes the deposited metal to have a bright 
surface. If the current is too strong, and the deposition 
too rapid^ the deposited metal is grayish and crystalline. 

In silvering or gilding objects of iron it is usual first 
to plate them with a thin caatrnjj of copper. In gilding 



CHAP. XI.] ELECTRICITY AND MAGNETISM. 



399 



base metals, such as pewter, they are usually first 
copper-coated. The gilding of the insides of jugs and 
cups is effected by fillirtg the jug or cup with the gilding 
solution, and suspending in it an anode of gold, the vessel 
itself being connected to the — pole of the battery. 




Fig. 159- 

Instead of a battery. a thermo-electric generator (Art. 
384), or a dynamo-electric generator (Art. 408), is now 
frequently employed. 

422. Metallo-chromy.— In 1826 Nobili discovered that when 
a solution of lead is electrolysed a film of peroxide of lead forms 
upon the anode. If this be a sheet of metal, — a plate of 
polished steel, for instance, — placed horizontally in the liquid 
beneath a ^platinum wire as a kathode, the deposit takes place 
in symmetrical rings of varying thickness, the thickest deposit 
being at the centre. These rings, known as Nobili's rings, 
exhibit all the tints of the rainbow, owing to interference of 
the waves of light" occurring in th^ film causing rays of different 
■wave-te^ngth and colour to be suppressed at different distances 
from the centre The colours form, in fact, in reversed order,' 
the ** colours of thin plates" of Newton's rings. According 
to Wagner this production of chromatic effects by electrolysing 
a solution of lead in caustic soda, is applied in Nuremberg to 
ornament metallic toys. The author of these Lessons has 
observed that when Nobili*s rings are made in a magnetic 



400 



ELEMENTARY LESSONS ON [chap, xu 



field they are no longer circular, the depositing currents being 
drawn aside in a manner which could be predicted from the 
observed action of magnets on conductors carrying currents. 

422 (dts). Electro - Chemical Power of Metals. — The 
following Table gives the electromotive -force of the different 
metals as calculated by the method of Art. 414 from their 
electro • chemical equivalents (Art. 212), and from the heat 
evolved by the combination with oxygen of a portion of the 
metal equivalent electro-chemically in amount to one gramme 
of hydrogen. The electromotive - forces (in volts) as observed 
fin dilute sulphuric acid) are added for comparison. 





Heat of 


E. M. F 


calculated. 


E. M. F. 


Substance. 








Equivalent. 


Relatively 
to Oxygen. 


Relatively 
to Zinc. 


observed. 


Potassiom . . 


69,800 


301 


+ 1 18 


+ 113 


Sodium . 




67,800 


2'9I 


+ 1-09 




Zinc . . 




42,700 


1-83 


O* 


o- 


Iron . . 




34,120 


I'SS 


- 0-28 


... 


Hydrogen 




34,000 


I '47 


-036 


... 


Lead . , 




25,100 


112 


-071 


-0-54 


Copper . 




18,760 


•80 


- I -08 


- 1-047 


Silver . . 




9,000 


•39 


- 1*44 


... 


Platinum . 




7,500 


•33 


-I -50 


-1-53 


Carbon 




2,000 


•09 


- 174 




Oxygen . 







0' 


-1-83 


-.i'-8s 


(Nitric Acid) . 


- 6,000 


- 0*26 


- 2*09 


-1-94 


(Black Oxide of 
Manganese) 


- 6,500 


- 0*29 


- 212 


- 2*23 


(Peroxide of Lead) 


-12,150 


- 0*52 


-2-35 


-2-52 


(Ozone) . . . 


- 14,800 


- •63 


- 2*46 


- 2 64 


(Permanganic 
. Acid) . .. . 


- 25,070 


- 1*09 


- 2*92 


-3-03 



The order in which these metals are arranged is in fact nothing else than 
the order of oxidisability of the metals (in the presence of dilute sulphuric 
acid) ; for ihat metal tends most to oxidise wtilch can, by oxidising, give out 
the most energy. It also shows the order in which the metals stand in their 
power to replace one another (in a solution containing sulphuric acid.) In 
this order too, the lowest on the list first, are the metals deposited by an 
electric current from solutions containing two or more of them : for that 
metal comes down first which requires the least expenditure of energy to 
?f^parat« it fropi. the- elements wiih which it was combined 



CHAF- xn.l ELECTRiCITV AND MAGNE^.^M. 



CHAPTER XIL 

Telegraphs and Telephones. 

Lesson XXXIX.— Electric Telegraphs. 

423. The Electric Telegraph* — It is difficult to asagn the 
invention of the Telegraph to any particular inventor. Lesage 
(Geneva, 1774), Lomond (Paris, 1787), and Sir F. Ronalds 
(London, 18 16), invented systems for transmitting signals 
through \rires by observing at one end the divergence of a pair 
of pith-balls when a charge of electricity was sent into the other 
end. Cavallo (London, 1795) transmitted sparks from Leyden 
jars through wires ** according to a settled plan." Soemmering 
(Munich, 1808) established a telegraph in which the signals 
were made by the decomposition of water in voltameters ; and 
the transmission of signals by the chemical decomposition of 
substances was attempted by Coxe, R. Smith, Rain, and others. 
Ampere (Paris, 1821) suggested that a galvanometer placed at 
a distant point of a circuit might serve for the transmission of 
signals. Schilling and Weber (Gottingen, 1833) employed the 
deflections of a galvanometer needle moving to right or left to 
signal an alphabetic code of letters upon a single circuit 
Cooke and Wheatstone (London, 1837) brought into practical 
application the first form of their needle telegraph. Henry 
(New York, 1831) utilised the attraction of an electromagnet 
to transmit signals, the movement of the armature producing 
audible soimds according to a certain code. Morse (New York, 
1837) devised a telegraph in which the attraction of an arma- 
ture by an electromagnet was made to mark a dot or a dash 
upon a moving strip of paper. Steinheil (Munich, 18-37) 
discoveied that instead of a return- wire the earth might be used, 
contact being made to earth at the two fends by means of earth 



402 



ELEMENTARY LESSONS ON [chap, xii. 



plates (see Fig, 162) sunk in the ground. Gintl (1853) ^^^d 
Stearns (New York, 1870) devised methods q{ duplex signalling. 
Stark (Vienna) and Bosscha (Leyden, 1855) invented diplex 
signalling, and Edison (Newark, N. J., 1874) invented quad- 
mplex telegraphy. For fast-speed work Wheatstone devised his 
automatic transmitter, in w^hich the signs which represent the 
letters are first punched by machinery on strips of paper ; these 
are then run at a great speed through the transmitting instru- 
ment, which telegraphs them off at a much greater rate than if 
the separate signals were telegraphed by hand. Hughes devised 
a type-printing telegraph. Wheatstone invented an ABC tele- 
graph in which signals are spelled by a hand which moves over 
a dial. For cable-working Sir W. Thomson invented his mirror 
galvanometer and his, delicate siphon-recorder. It is impossible 
in these Lessons to describe more than one or two of the 
simpler and more frequent forms of telegraphic" instruments. 
Students desiring further information should consult the excel- 
lent manuals on Telegraphy by Messrs. Preece and Sivewright, 
and by Mr. Culley. 

424. Single -Needle Instrument. — The single-- 
needle instrument (Fig, 160) consists essentially of a 

vertical galvan-* 

ometer, in which 

a lightly hung 

magnetic needle 

is deflected to 

right or left 

when a current 

is sent, in one 

direction or the 

other, around a 

coil surrounding 

the needle ; the 

needle visible in 

front of the dial 

^'^' '^°- is but an index, 

the real magnetic needle being behind. A code of 

movements agreed upon comprises the whole alphabet 

in combinations of motions to right or left. In order 




CHAP. XII.] ELECTRICITY AND MAGNETISIM. 403 

to send currents in either direction through the circuit. 
a ''signalling-key" or "tapper" is usually employed. 
The tapper at one end of the line works the instru- 
ment at the other ; but for the sake of convenience it 
is fixed to the receiving instrument. In Fig. 160 the 
two protruding levers at the base form the tapper, and 
by depressing the right hand one or the left hand one, 
currents are sent in either direction at will. 

The principle of action will be made more clear by 
reference to Fig. 161, which shows a separate signalling 
key. The two 
horizontal levers 
are respectively 
in communica- 
tion with the 
'Mine," and with 
the return - line 
through "earth." 
When not in use 

they both spring Fig. jgi. 

up against a cross 
strip of metal joined to the zinc pole of the battery. 
Below them is another cross strip, which communicates 
with the copper (or + ) pole of the battery. On 
depressing the "line" key the current runs through the 
line and back by earth, or in the positive direction. 
On depressing the " earth " key (the line key remaining 
in contact with the zinc-connected strip), the current 
runs through the earth and back by the line, or in the 
negative direction. Telegraphists ordinarily speak of 
these as positive and negative currents respectively. 

As it is necessary that a line should be capable of 
being worked from either end, a battery is used at each, 
and the wires so connected that when at either end a 
message is being received, the battery circuit at that end 
shall be open. Fig. 162 shows the simplest possible 
case Qf syich an arrangement. At one end is a battery 




404 



ELEMENTARY LESSONS ON [chap, xii. 



zc^ one pole of which is put to earth, and the other com- 
municates with a key K. This key is arranged (like that 
in Fig. 164), so that when it is depressed, so as to send 
a signal through the line, it quits contact with the 
receiving instrument at its own end. The current 
flowing through the line passes through K' and enters a 




Fig. 162. 

receiving instrument G' at the distant end, where it pro* 
duces a signal, and returns by the earth to the battery 
whence it started. A similar battery and key at the 
distant end suffice to transmit signals in the opposite 
direction to G when K is not depressed. The diagram 
is drawn as if G were a simple galvanometer ; but the 
arrangement would perfectly suit the Morse instrument, 
in which it is only required at either end to send long 
and short currents without reversing the direction. 

425. The Morse Instrument. — The most widely 
used instrument at the present day is the Morse. The 
Morse instrument consists essentially of an electro- 
magnet, which, when a current passes through its coils, 
draws down an armature for a short or a long time. 



CHAP. xiLj ELECTRICITY AND MAGNETISM. 405 

It* may either be arranged as a ^^ sounder ^'^ in which 
case the operator who is receiving the message listens 
to the clicks and notices whether the intervals between 
them are long or short; or it may be arranged as an 
** embosser^^ to print dots and dashes upon a strip of paper 
drawn by clockwork through the instrument. In the 
most riiodern form, however, the Morse instrument is 
arranged as an ^^ ink-writer ^^ in which the attraction of 
the armature downwards lift? a little inky wheel and 
pushes it against a ribbon of paper. If the current is 
momentary it prints a mere dot. If the current con- 
tinues to flow for a longer time the ribbon of paper moves 
on. and the ink- wheel marks a dash. The Morse code, 
or alphabet of dots and dashes, is as follows : — 



A.— 
B — • • • 
c — . — . 
D — . . 
E . 


K — .— 
L . — . . 

M 

N — . 




U. . — 
V . . . — 

w. 

X — 


F . 

G 

H • • • • 

I . . 
J 


P . 

Q 

R .— . 

^ • • • 

T — 


Z . . 

Full stop 

Repetition , . — — .^ . 
HjTphen — , , . . — 
Apostrophe ■, — . 



426. Belay. — In working over long lines, or where 
there are a number of instruments on one circuit, the 
currents are often not strong enough to work the 
recording instrument directly. In. such a case there is 
interposed a relay or repeater. This instrument con- 
sists of an electromagnet round which the line current 
flows, and whose delicately poised armature, when 
attracted, makes contact for a local circuit in which a 
local battery and the receiving Morse instrument are 
included. The principle of the relay is, then, that a 
cun-ent too weak to do the work itself may set a strong 
local current to do its work for it. 



4o6 



ELEMENTARY LESSONS ON [chap, xil. 



In Fig, 163 is shown a Morse instrument (an "em- 
bosser "^ M, joined in circuit with a local battery B, and 




Tig^ 165. 

a relay. Whenever a current in the line circuit moves 
the tongue of the relay it closes the local circuit, and 
causes the Morse to record either a dot or a dash upon 
the strip of paper. The key K is shown in an . enlarged 

K 




Fig. 164. 

view in Fig. 164. The line wire is connected with the 
central pivot A. K spring /keeps the front ,en4 of the 
key elevated when not in use, so that the line wire is in 



CHAP. XII.] ELECTRICITY AND MAGNETISM. 407 

communication through the rear end of the key with the 
relay or receiving instrument. Depressing the key breaks 
this communication, and by putting the Une wire in com- 
munication with the main battery transmits a current 
through the line, 

427. Faults iu Telegrapli Lines. — Faults may 
occur in telegraph lines fiom several causes : either from 
the breakage of the wires or conductors, or from the 
bieakage of the insulators, thereby short-circuiting the 
current through the eaith before it reaches the distant 
station, or, as in overhead ^^ires, by two conducting 
\nres touching one another. Various modes for testing 
the existence and position of faults are known to telegraph 
engineers ; they depend upon accurate measurements of 
resistance or of capacity. Thus, if a telegraph cable part 
in mid-ocean it is possible to calculate the distance from 
the shore end to the broken end by comparing the resist^ 
ance that the cable is known to offer per mile with the 
resistance offered by the length up to the fault, and divid- 
ing the latter by the former. 

428. Duplex Telegraphy. — There are two distinct 
methods of arranging telegraphic apparatus so as to 
transmit two messages through one wire, one from each 
end, at the same time. The first of these, known as 
the differential method^ involves the use of instruments 
wound with differential coils, and is applicable to special 
cases. The second method of duplex working, known 
as the Wheatsiojie's Bridge Method^ is capable of much 
more general application. The diagram of Fig. 165 
will explain the general principle. The first require- 
ment in duplex working is that the instmment at each 
end shall only move in response to signals from the 
other end, so that an operator at R may be able to 
signal to the distant instrument M' without his own 
instrument M being affected, M being all the while in 
circuit and able to receive signals from the distant 
operator at R'. To accomplish this the circuit is 



4o8 



ELEMENTARY LESSONS ON [chap. xil. 



divided at R into two branches, which go, by A and 
B respectively, the one to the line, the other through 
a certain resistance P to the earth. If the ratio 
between the resistances in the arms RA and RB is 
equal to the ratio of the resistances of the line and of 
P, then, by the principle of Wheatstone's Bridge, no 
current will pass through M. So M does not show any 
currents sent from R ; but M' will show them, for the 
current on arriving at C will divide into two parts, part 
flowing round to the earth by R', the other part flowing 




Fjj^. 165. 

through M' and producing a signal. If, while this is 
going on, the operator at the distant R' depresses his 
key and sends an equal current in the opposite direction, 
the flow through the line will cease ; but M will now 
show a signal, because, although no current flows 
through the line, the current in the branch RA will 
now flow down through M, as if it had come from the 
distant R', so, whether the operator at R be signalling 
or not, M will respond to signals sent from R'. 

The Diplex method of working consists in sending 
two messages at once through a wire in the same direc- 
tion. To do this it is needful to employ instruments 
which work only with currents in one given direction. 
The method involves the use of " relays *' in which the 
armatures are themselves permanently magnetised, (or 
"polarised"), and "\Vhich therefore respond only to 
currents in one direction. 

The Quadruplex method of working combines the 



CHAP. XII.] ELECTRICITY AND iMAGNETISM. 409 

duplex and the dipTex methods. On one and the same 
line are used two sets of instruments, one of which 
(worked by a ** polarised" relay) woiks only when the 
direction of the current is changed, the other of which 
(worked by a non-polarised relay adjusted with springs 
to move only with a certain minimum force) works only 
when the sirength of the current is changed and is inde- 
pendent of their direction. 

429. Submarine Telegraphy. — Telegraphic com- 





Fig. 166. 

munication be*tween two countries separated by a strait 
or ocean is carried on through cables, sunk to^the 

2 £ 



410 ELEMENTARY LESSONS ON [chap. xn. 

bottom of the sea, which carry conducting v/ires care- 
fully protected by an outer sheath of insulating and 
protecting materials. The conductor is usually of purest 
copper wire, weighing. from 70 to 400 lbs. per nauti- 
cal mile, made in a sevenfold strand to lessen risk 
of breaking. Fig. 166 shows, in their natural size, 
portions of the Atlantic cables laid in 1857 and 1866 
respectively. In the latter cable, which is of th^e usual 
type of cable for long lines, the core is protected first by 
a stout layer of guttapercha, then by a woven coating of 
jute, and outside all an external sheath made of ten iron 
wires, each covered with hemp. The shore ends are even 
more strongly protected by external wires. 

430. Speed of Signalling * tdarough Cables. — 
Signals transmitted through long cables are retarded, the 
retardation being due to two causes. 

Firstly^ The self-induction of the circuit may prevent 
the current from rising at once to its height, the retarda- 
tion being expressed by Helmholtz^s equations, given in 
Art. 405. 

Secondly^ The cable in its insulating sheath, when 
immersed in water, acts Hke a Lej'^den jar of enormous 
capacity (as explained in Art. 274), and the first portions 
of the current, instead of flowing through, remain in the 
cable as an electrostatic charge. For every separate 
signal the cable must be at least partially charged and 
then discharged. CuUey states that \^hen a current is 
sent through an Atlantic cable from Ireland to New- 
foundland no efiFect is produced on the most delicate 
instrument at the receiving end for two-tenths of a 
second, and that it requires three seconds for the current 
to gain its full strength, rising in an electric wave which 
travels forward through the cable. The strength of the 
current falls gradually also when the circuit is broken. 
The greater part of this retardation is due to electrostatic 
charge, not to electromagnetic self-induction ; the re- 
tardation being proportional to the square of the length 



CHAP. XII.] ELECTRICITY AND MAGNETISM. 411 

of tbe cable. The various means adopted to get rid of 
this retardation are explained in Art. 275, 

431. Receiving Instruments for Cables. — The 
mirror-galvanometer of Sir W. Thomson (Art. 202) was 
devised for cable signalling, the movements of the sptft 
of light sweeping over the scale to a short or a long 
distance sufficing to signal the dots and dashes of the 
Morse code. The Siphon Recorder of Sir W. Thonvs<M> 
is an instrument which writes the signals upon a strip dl 
paper by the following ingenious means : — The needle 
part of a powerful and sensitive galvanometer is replaced 
by a fine siphon of glass suspended by a silk fibre, one 
end of which dips into an ink vessel The ink is spurted 
without friction upon a strip of paper (moved by clock- 
work vertically past the siphon), the spurting being 
accomplished electrically by charging the ink vessel by 
a continuous electrophorus, which is itself worked by a 
small electromagnetic engine. 

Lesson XL. — Electric Bells ^ Clocks^ and Telephones. 

482. Electric Bells. — The common form of E^lectric 
Bell or Trembler consists of an electromagnet, which 
moves a hammer backward and forward by alternately 
attracting and releasing it, so that it beats against a bell. 
The arrangements of the instrument are shown in Fig. 
167, in which E is the electromagnet and H the hammer, 
A battery, consisting of one or two Leclanchd cells placed 
at some convenient point of the circuit, provides a current 
when required. By touching the " push " P, the circuit 
is completed, and a current flows along the line and 
round the coils of the electromagnet^ which forthwith 
attracts a small piece of soft iron attached to the lever, 
which terminates in the hammer H. The lever is itself 
included in .the circuit, the <:urrent entering it above and 
quitting it at C by a contact-breaker, consisting of a 
api'ing tipped with platinum resting against the platintun 



412 



ELEMENTARY LESSONS ON [chap. xii. 



tip of a screw, from which a return wire passes back to 
the zinc pole of the battery. . As soon as the lever is 
attracted forward the circuit is broken at C by the spring 
moving away from contact with the screw; hence the 
current stops, and the electromagnet ceases to attract the 
armature. The lever and hammer therefore fall back,' 



^..nnnr^I^52"inn 




Fig, 167, 

again establishmg contact at C, whereupon the hammer 
is once more attracted forward, and so on. The push 
P is shown in section on the right of Fig. -167. It 
usually consists of a cylindrical knob of ivory or porcelain 
capable of moying loosely through a hole in a circular 
support of porcelain or wood, and which, when pressed, 
forces a platinum -tipped spring against a metal pin, and 
so makes electrical contact between the two partsipf the 
interrupted circuit 

433. Electric Clocks.— Clocks may be either driven 
or controlled by electric currents. Bain, Hipp, and 
others,, have devised electric clocks of. the first kind, in 
which the ordinary motive power of a weight or spring is 



CHAP. XII.] ELECTRICITY AND MAGNETISM. 413 



abandoned, the clock being driven by its pendulum, the 
" bob " of which is an electromagnet alternately attracted 
from side to side. The difficulty of maintaining a perfectly 
constant battery current has prevented such clocks from 
coming into use. 

Electrically controlled clocks, governed by a standard 
central clock, have proved a more fruitful invention. In 
these the standard timekeeper is constructed so as to 
complete a circuit periodically, once every minute or hali 
minute. The transmitted currents set in movement the 
hands of a system of dials placed at distant points, by 
causing an electromagnet placed behind each dial to 
attract an armature, which, acting upon a ratchet wheel 
by a pawl, causes it to move forward through one tooth 
at each specified interval, and so carries the hands round 
at the same rate as those of the standard clock. 

Electric chronographs are used for measuring very small in- 
tervals of time. A style fixed to thp armature of an electro- 
magnet traces a line upon a piece of paper fixed to a cylinder 
revolving by clockwork. A current sent through the coils of 
the eleciromagnet moves the armature and causes a lateral notch 
in the line so traced. Two currents are marked by two notches ; 
and from thw interval of space between the two notches the in- 
terval of time which elapsed between the two currents may be 
calculated to the ten-thousandth part of a second if the speed 
of rotation is accurately known. The velocity with which a 
cannon ball moves along the bore of the cannon can be measured 
thus. 

434. Electric Telephones — The first successful 
atteinpt to transmit sounds electrically was made in 
1 86 1 by Reis, who succeeded in conveying musical and 
other tones by an imperfeci telephone. In this instru- 
ment the voice was cau.^-ed to act upon a point of loose 
contact in an electric circuit, and by bringing those parts 
into greater or less intimacy of contact (Art. 346), thereby 
varied the resistance offered to the circuit. The trans- 
mitting part of Reis's telephone consisted of a batter)* 
and a contact-breaker, the latter being formed of a tym- 



4X4 ELEMENTARY LESSONS ON [chap, xii 

panum or diaphragm of stretched membrane, capable of 
taking up sonorous vibrations, and having attached to 
it a thin elastic strip of platinum, which, as it vibrated, 
beat to and fro against the tip of a platinum wire, so 
making and breaking contact wholly or partially at each . 
vibration in exactly the same manner as is done with the 
carbon contacts in the modern transmitters of Blake, 
Berliner, etc. The receiving part of the instrument 
consisted of an iron wire fixed upon a sounding-board 
and surrounded by a coil of insulated wire forming part 
of the circuit. The rapid magnetisation and demag- 
netisation of such an iron core wil) produce audible 
sounds (Art. 113), which, since the pitch of a note 
depends only on the frequency and not on the form or 
amplitude of the vibrations, will reproduce the pitch of a 
note sung Into the transmitting part. If the current varj* 
less abruptly, the iron wire is partially magnetised and 
demagnetised, giving rise in turn to vibrations of varying 
amplitudes and forms ; hence such a wire will serve 
perfectly as a receiver to reproduce speech if a good 
transmitter is used. Reis himself transmitted speech 
with his instrument, but only imperfectly, for all tones 
of speech cannot be transmitted by abrupt interruptions 
of the current, to which Reis's transmitter is prone when 
spoken into, owing to the extreme lightness of the con- 
tact : they require gentle undulations, sometimes simple, 
sometimes complex, according to the nature of the sound. 
The vowel sounds are produced by periodic and complex 
movements in the air ; the consonants being for the most 
part non-periodic. If the parts in contact be not too 
light, and speech be not too loud, Reis's transmitter 
works fairly as a transmitter, the platinum contacts when 
clean serving as a satisfactory current-regulator to vary 
the current in proportion to the vibrations of the voice. 

Reis also devised a second receiver, in which an electro-magnet 
attracted an elastically-supported armature of iron, which vibrated 
under the attraction of the more or less interrupted current. 



CHAP. XII.] ELECTRICITY AND MAGNETISM. 415 



435. G-rsiihain BelFs Telephone. — In 1876 Graham 
Beil invented the magneto-telephone. In this instrument 
the speaker talks to an elastic plate of thin sheet iron, 
which vibrates and transmits its every movement electric- 
ally to a similar plate ill a similar telephone at a distant 
station, causing it to vibrate in an identical manner, and 
therefore to emit identical sounds. The transmission of 
the vibrations depends upon the principles of magneto- 
electric induction explained in Lesson XXXVI. Fig. 
168 shows Bell's Tele- 
phone in its latest form, 
and its internal parts in 
section. The disc D is 
placed behind a conical 
mouthpiece, to which the 
speaker places his mo^th 
or the hearer his ear. 
Behind the disc is a mag- 
net AA iTjnning the length 
of the instrument*; and 
upon its front pole, wjiich 
nearly touches the disc, 
is fixed a small bobbin, 
on which is wound a, coil C of fine insulated wire, the 
ends of the coil being connected with the terminal screws 
F F. One such instrument is used to transmit, and one 
to receive, the sounds, the two telephones being con- 
nected in simple circuit. No battery is needed, for the 
transmitting instrument itself generates the induced 
currents as follows : The magnet AA induces a certain 
number of lines-of-force through the coil C. Many of 
these pass into the iron disc. When the iron disc in 
vibrating moves towards the magnet-pole, more Hnes-df 
force meet it ; when it recedes, fewer Hnes-of-fofce meet 
it Its motion to and fro will therefore aUer the number 
of l77ieS'Of-force which pass through the hollow of the coil 
C, and will therefore (Art. 394) generate in the wire of 




Fig. 168. 



4i6 ELEMENTARY LESSONS ON [chap. xii. 



the coils currents whose strength is proportional to the 
rate of change in the number of the lines-of-force which 
pass through the coil. Bell's telephone, when used as 
a transmitter, may therefore be regarded as a sort of 
magneto-electric generator, which, by vibrating to and 
fro, pimips currents in alternate directions into the wire. 
At the distant end the currents as they arrive flow round 
the coils either in one direction or the other, and there- 
fore either add momentarily to or take from the strength 
of the magnet. When the current in the coils is in such 
a direction as to reinforce the magnet, the magnet attracts 
the iron disc in front of it more strongly than before. If 
the current is in the opposite direction the disc is less 
attracted and flies back. Hence, whatever movement is 
imparted to the disc of the transmitting telephone, the 
disc of the distant receiving telephone is forced to repeat, 
and it therefore throws the air into similar vibrations, 
and so reproduces the sound. Bell's Telephone, used 
as a receiver, differs only from the second receiver of 
Reis in having as its armature a thin elastic iron plate 
instead of an iron bar oscillating on an elastic support, 
and in having its central magnet of steel instead of 
iron. 

436. Edison's Telephone. — Edison constructed a 
telephone for transmitting speech, in which the vibrations 
of the voice, actuating a diaphragm of mica, made it 
exert more or less compression on a button of prepared 
lamp-black placed in the circuit. The resistance of this 
is affected by pressure of contacts ; hence the varying 
pressures due to the vibrations cause the button to offer 
a varying resistance to any current flowing (from a battery) 
in the circuit, and vary its strength accordingly. This 
varying current may be received as before in an electro- 
magnetic receiver of the type described above, and there 
set up corresponding vibrations. Edison has also in- 
vented a Telephone Receiver of singular power, which 
depends upon a curious fact discovered by himself, namely, 



CHAP. xiL] ELECTRICITY AND MAGNETISM. 417 

that if a platinum point presses against a rotating cylinder 
of moist chalk, the friction is reduced when a current 
passes between the two. And if the* point be attached 
to an elastic disc, the latter is thrown into vibratioms 
corresponding to the fluctuating currents coming from 
the speaker's transmitting instrument. 




Fig. 169. 

436 {bis). Dolbear's Telephone. — Telephone Re- 
ceivers have also been invented by Varley and Dolbear, 
in which the attraction between the oppositely-electrified 
armatures of a condenser is utilised in the production of 
sounds. The transmitter is .placed in circuit with the 
primary wire of a small induction-coil ; the secondary 
wire of this coil is united through the line to the receiving 
condenser. In Dolbear's telephone the receiver consists 
merely of two thin metal discs, separated by a very thin 
air-space, and respectively united to the two ends of the 
secondary coiL As the varjdng currents flow into and 
out of this condenser the two discs attract one another 
more or less strongly, and thereby vibrations are set 



418 ELEMENTARY LESSONS ON [CHAP, ^U. 

up which correspond to the vibrations of the original 
sound. 

437. Hughes' Microphone. — Hughes, in 1878, 
discovered that a loose contact between two conductors, 
forming part of a circuit in which a small battery and a 
receiving telephone are included, may serve to transmit 
sounds without the intervention of any specific tympanum 
or diaphragm like those of Reis and Edison, because the 
smallest vibrations will effect the amount of the resistance 
at the point of loose-contact, if the latter be delicately 
set. The Microphone (Fig. 169) embodies this prin- 
ciple. In the form shown in the figure, a small thin 
pencil of carbon is supported loosely between two little 
blocks of the same substance- fixed to a sounding-board 
of thin pine-wood, the blocks being connected with one 
or two small cells and a Bell telephone as a receiver. 
The amplitude of the vibrations emitted by this telephone 
may be much greater than those of the original sounds, 
and therefore the microphone may serve, as its name 
indicates, to magnify minute sounds, such as the ticking 
of a v/atch or the footfalls of an insect, and render them 
audible. The less sensitive carbon- transmitters^ used 
frequently in conjunction with the telephone, are some- 
times regarded as varieties of the microphone. In some 
of these instruments— Blake's, for instance — there is a 
tympanum like that of Edison's and of Reis's tele- 
phone. 

438. Hughes' Induction Balance. — The extreme 
sensitiveness of Bell's telephone (Art, 435) to the feeblest 
currents has suggested its employment to detect currents 
loo weak to affect the most delicate galvanometer. The 
currents must, however, be intermittent, or they will not 
keep the disc of the telephone in vibration. Hughes 
applied this property of the telephone to an instrument 
named the Induction Balance (Fig. 170). A small 
battery B, connected with a microphone M, passes 
through two coils of wire Pi, P,, wound on., bobbins fixed 



CHAP. XII.] ELECTRICITY AND MAGNETISM. 419 

on a suitable stand. Above each of these primary cx)ils 
are placed two secondary coils, Si, S2, of wire, of the 
same size, and of exactly «qual numbers of turns of wire. 
The. secondary coils are joined to a telephone T, and 
are Wound in opposite directions. The result of this 
arrangement is that whenever a current either begins or 
stops flowing in the primary coils, Pi induces a current 
in Sj, and P, in Sg. As Si and S^ are wound in opposite 
ways, the two currents thus induced in the secondary 
wire neutralise one another, and, if they are of equal 
strength, balance one another so exactly that no sound 





Pig. 170. 

is heard in the telephone. But a perfect balance cannot 
"be obtained unless the resistances and the co-efficients of 
mutual induction and of self-induction are alike. If a flat 
piece of silver or copper (such as a coin) be introduced 
between Si and P^ there will be less induction in Si than 
in Sg, for part of the inductive action in P^ is now spent 
on setting up currents in the mass of the metal (Art. 401), 
and a sound will again be heard in the telephone. But 
balance can be restored by moving Sg farther away from 
Ps, until the induction in S2 is reduced to equality with 
Si, when the sounds in the telephone again cease. It is 
possible by this means to test the relative conductivity of 
different metals which are introduced into the coils. It 
is even possible to detect a counterfeit coin by the indi- 



420 



ELEMENTARY LESSONS. [chap. xii. 



cation thus afForded of its conductivity. The induction 
balance has also been applied in surgery by Graham 
Bell to detect the presence of a bullet in a wound, for a 
lump of metal may disturb the induction when some 
inches distant from the coils. 




Fig. 171. 



430. Hughes' Magnetic Balance. — ^A very con- 
venient instrument for testing the magnetic properties 
of different specimens of iron and steel was devised by 
Hughes in 1884. The sample to be tested is placed in 
a magnetising coil A (Fig. 171), and a current is sent 
round it. It deflects a lightly-suspended indicating 
needle B, which is then brought to zero by turning a 
large compensating magnet M upon its centre. A small 
coil G is added to balance the direct deflecting effect 
due to coil A. The author of this book has shown that 
if the distance from M to B is 2-3 times the length of 
M, the angle through which M is turned is proportional 
to the magnetic force due to the iron core at A, provided 
the angle is less than 60**. 



CKAP. XIII.] ELECTRICITY AND MAGNETISM. 421 



/ 
/ 



CHAPTER XIII. 

Wireless Telegraphy. 

Marconi's Triumph— He Startles the World by Sending a Wire- 
less Message Across the Atlantic — Marconigrams on Ocean 
Liners— ^ Yacht Races, etc. 

Lesson XLI. — Ether Waves. 

440. — Professor Morse, the inventor of the first prac- 
tical telegraph, seems also to have sent electric signals 
without wire, in 1842, over a distance of eighty feet, 
and in 1854 Lindsay of Dundee, Scotland, signaled 
over a distance of two miles. But although these 
experiments were on the right track, even Preece in 
England and Edison were unable to make much head- 
way in this direction, until Hertz had made his epoch- 
making discovery. 

441. Hertzian Waves. — In the seventeenth century 
Hughens proclaimed the existence of ether and the 
undulating motion of light, but during the whole of 
the eighteenth century no progress was made, except 
a confirmation by Dr. Thomas Young. In the nine- 
teenth century the oscillatory nature of a discharge of 
a Leyden jar was recognised by such eminent author- 
ities as Henry, Helmholtz and Kelvin, while Clerk 
Maxwell, who died 1879, contended that the velocities 
of electric and light waves are nearly or exactly the 
same, that therefore the media through which they are 
transmitted must necessarily occupy the same space 
and must be identical, and the difference between the 
two must consist in, or be based on, the difference in 
the length of their respective waves. 




422 ELEMENTARY LESSONS ON [chap. xiii. 

This genial theory was destined to be proved correct 
by Professor Hertz, who in 1886 discovered acciden- 
tally, while experimenting with a Leyden jar and two 
coils of wire, each of which had a 
spark gap, that a disruptive discharge 
from a Ruhmkorff coil through one 
of the coib would induce an appre- 
ciable current in the other coil. This 
response was in the form of a minute 
spark. Fig. 172 shows the simple 
shape of such a coil with a spark 
Fig. 172. g^p, called a wave detector. 

It is a duty we owe to genius to insist upon the merit 
of such a discovery. What the igniting spark is to 
the charge in a gun, that much and no less is the dis- 
covery of a new truth to science. By his discovery 
Hertz was able to prove Clerk MaxwelTs theory to be 
correct; and going further, he demonstrated that the 
electromagnetic waves can be reflected from conducting 
surfaces, just as waves of light are reflected from pol- 
ished surfaces, and that they can be refracted hy dielec- 
tric substances, just as waves of light are refracted 
through prisms of glass. 

442. Ether and Ether Waves. — To the three familiar 
divisions of matter, solid^ liquid, and gas, science has 
added a fourth, ether, which is supposed to be present 
everywhere, even in the densest substances, as gold or 
platinum, surrounding each molecule. The relation 
of ether to the molecules surrounded by it has been 
compared to that of a jelly to lead bullets contained 
in it. If the jelly is made to oscillate slightly but very 
rapidly, the bullets will seem to lie perfectly still. 
Their inertia is so great, as compared with that of the 
jelly, that a forward motion of the jelly cannot over- 
come it before the next backward motion of the jelly 
has set in and has neutralized the first impulse. 

The ether, present in the atmospheric air as well as 
anywhere else, may be set into vibration; that is, it 
niay be made to move in waves like the surface of a 
body of water. If we strike the surface of a pool of 
water at one side with a stick, waves will be seen to 
run in concentric circles across the pool, and if we 



CHAP. XIII.] ELECTRICITY AND MAGNETISM. 



423 



repeat the stroke in a certain eve;i rhythm, the waves 
will grow higher and higher up to a certain limit, and 
will run farther and farther. But if the strokes are 
made at irregular intervals, this increase will give way 
to a decrease, because the waves interfere with each 
other. If we place a square piece of wood so on the 
surface of a bod}'- of still 



water that a spring (see 
Fig- 173) will allow it to 
move up and down with 
the slightest wave, it is 
evident that we can adjust 
the strokes on the other 
side of the water so as to 
correspond or harmonise 
with the resiliency of the 
apparatus, which is deter- 




Figr. 173. 



mined by the power of the spring and the weight 
of the piece of wood. This rate, by the way, is 
always the same for each apparatus; that is to say, 
whether the wood oscillates slowly through a small 
space or rapidly through a greater space, the number 
of oscillations in a given time remains the same. 
Adjusting the strokes upon the surface of the water to 
the rate of the apparatus is termed ''attuning'^ or 
''synchronising^ Repeated attuned strokes will cause 
the oscillations of the wood to increase in length. In 
exactly the same way the waves of the ether may be 
attuned to a receiver placed at a great distance, and 
on this quality of the ether wireless telegraphy is 
based. 

443. Electricity and Inertia. — When light or elec- 
tricity is called wave Tuotion in ether^ the term wave^ 
therefore, signifies ''a disturbance periodic both in space 
and timey This definition includes sound waves as 
well as the waves of the ocean. The ether, like water 
and air, in order to be capable of transmitting wave 
motion, must necessarily possess two properties: elas- 
ticity in order to be able to store up energy and to 
effect recoil, and inertia in order that the disturbed 
medium may be carried beyond the mark, and may 
oscillate across it until it finds its equilibrium, like a 



424 ELEMENTARY LESSONS ON [chap. xiii. 

violin string pulled, or a pendulum. The oscillatory 
nature of a discharge of a Leyden jar was known 
before Clerk Maxwell, who stated his theory in sub- 
stance as follows: 

* ' The elastic displacement corresponds to electro-static 
charge {pr^ roughly speakings to electricity) ; the inertia 
corresponds to magnetism. ' ' 

The drawing aside of the violin string corresponds 
here to the charging of the Leyden jar; letting go the 
string is analogous to suddenly discharging the jar; 
for the recoiling of the strained dielectric causes a 
current, the inertia of which causes it to more than 
empty the apparatus, so that for an instant the charge 
of the jar is reversed^ as from a -f charge to a — charge. 
Consequently the current flows backwards, charging 
the jar in the same sense as at first; then the current 
flows out again, and so forth in rapid oscillations, until 
the equilibrium is found, or, in other words, until all 
the energy is dissipated (converted into heat). (Art. 
295.) These oscillations of electricity, several millions 
of which occur in one minute, are communicated to 
the ether, just as sound waves are transmitted through 
air from a tuning-fork to the ear. 

Man has no organ by means of which he can per- 
ceive the ether waves described above. Sound waves 
which vibrate from 40 to 40,000 times per second are 
audible to the human ear; the retina of the human eye 
responds to vibrations between 4000 billions and 
7000 billions per second. The large gap between 
these two kinds of vibrations is partly or entirely filled 
up by electric oscillations. The simple device needed 
for perceiving or detecting these electric oscillations 
or disturbances consists in a pair of wire coils, adjusted 
so that when immersed in strong electric radiation they 
give minute sparks across a minute air gap. 

Lesson XLIL — Wireless Telegraph Apparatus. 

444. The Coherer. — Simultaneously with the Hertzian 
waves another important discovery was made by Cal- 
zecchi Onesti, namely that metal filings can be made 
to cohere by the sudden discharge of an electrified 



CHAP, xm.] ELECTRICITY AND MAGNETISM. 425 

coil of wire. The laws governing this phenomenon 
were formulated by Branly in 1890, who produced a 
filings coherer that was sensitive to Hertzian waves, 
and in 1894 Dr. Lodge improved the coherer by 
enclosing the filings in a vacuum, and applied to it the 
principles of electrical resonance. The laws govern- 
ing high frequencies and great pressures were given to 
the world preeminently by Tesla, who also invented 
methods for the production and proper insulation of 
high potentials. 

A coherer may be considered as a group of very 
small condensers arranged in series parallel, each pair 
of particles being separated by a thin coating of oxide, 
and forming opposite sides of an elementary con- 
denser, the capacity of the whole being very small. 
In a coherer connected in series with the receiving 
antennse charged by induction, the difference of poten- 
tial across the coherer may cause a spark to pass. 
This spark passes from particle to particle, tearing off 
at each gap a small part of the coating, thus bringing 
the particles into metallic contact. A slight tap on 
the coherer displaces the particles again, breaking the 
metallic contact. A coherer is a means of obtaining 
considerable difference of potential, and at the same 
time an instrument for indicating this. 

Marconi's silver coherer has a tube one and one-half 
inches in length, and one-twelfth inch internal diam- 
eter. (See Fig. 174.) ^ 
Two pieces of silver f ^ , =^ 
wire, one-fifth inch long, 
are tightly plugged in, 
leaving a central space 
between them one-thirtieth inch long and contain- 
ing a powder composed of ninety parts nickel 
filings and ten parts silver filings, all coated with an 
infinitely light coating of mercury. The tube is 
sealed. A perfect vacuum is not required, but desir- 
able. A greater percentage of silver filings, or a 
shorter space between the plugs of silver wire, will 
increase the sensitiveness of this coherer. 

445. Marconi's System. — Marconi succeeded in com- 
bining all these discoveries in a system which enabled 




426 ELEMENTARY LESSONS ON [chap. xili. 

him to send signals across the Atlantic Ocean, the first 
of which was sent from Poldhu, Cornwall, England, 
and received on Signal Hill, St. Johns, Newfoundland. 
It consisted in several repetitions of the three short 
marks representing the letter S in the telegraphic 
code. The date of this most remarkable feat of modern 
times was December 12, 1901. In order to show the 
unlimited possibilities of this greatest of all recent 
achievements of the human mind, we will mention 
here that Marconi subsequently succeeded in trans- 
mitting across the ocean, simultaneously, and by 
means of two transmitting antennae wires placed close 
together, two messages, one in English and one in 
French. We will now proceed to a description of the 
apparatus used in wireless telegraphy, aided by dia- 
grams. Figs. 175 and 176. 

Hertzian waves pass without appreciable hindrance 
through doors and walls and, generally, non-conduct- 
ing bodies, being only arrested by metals and other 
conductors; but in wireless telegraphy, hills, trees and 
buildings seem to partake of the nature of metals, and 
largely absorb the waves, just as light passes through 
a thin sheet of glass but is arrested by a thick sheet. 
If, nevertheless, Marconi and others have succeeded in 
transmitting messages from one station to another, 
between which a hill over 800 feet high intervened, 
when the vertical wires were only 170 feet high, it 
must be assumed that the waves went over, not 
through, the hill. It seems to be an established fact 
that waves can be sent one-third farther over land 
than over sea by the same apparatus, but the subject is 
still very uncertain. Marconi claims that it is just as 
easy to work at high speed across the ocean as to work 
across the English Channel, and he is confident of 
establishing direct communication between England 
and New Zealand. The curvature of the earth, he 
says, does not affect the signals, and ultimately it will 
be possible to send them all around the globe. The 
invention is certainly full of consequences. There are 
fourteen telegraph cables across the Atlantic, and 
nearly eighteen hundred in the whole world, costing 
about $1000 a mile and requiring a large number of 



CHAP. XIII.] ELECTRICITY AND MAGNETISM 



427 



cable steamers for their laying and repairing. All 
these may soon be replaced by Marconi stations, 
one of which can be built and equipped for 
g6o,ooo. 

446. Transmitter of Wireless Message. — In Fig. 175 B 
is a battery, K the transmission key, P the primary 
winding of an induction coil, L its secondary winding, 
C a condenser, S the spark gap between the two elec- 




Traa/sm/tt/a/g Station 



^ R£C£/V/A/6 STAT/OAf 



,trodes T T,P2 the primary and L2 the secondary wind- 
ing of another induction coil, E the earth, H a 
movable pointer, D a variable inductive resistance, A 
the vertical transmitting wire. 

The condenser C is used for the synchronising or 
attuning of the apparatus, while the second induction 
coil serves to greatly increase the intensity of the 
waves that oscillate in the spark gap.- 

447. Receiver of Wireless Message. — In Fig. 175 ^z is 
the vertical wire connected, through the inductive 
resistance dy changeable by moving the pointer h and 
primary coil / of a transformer, with the earth. These 
parts may be said to represent the load of the wood in 
Art. 442. Their joint oscillation, caused by the waves 
transmitted through space, are increased in the second- 
ary winding //, the two parts of which are separated 
by a condenser ^, which is analogous to the spring in 
Fig- 173- Either d and p ox c may be changed in 
tuning the receiver. Even with the increase by means 
of the induction coil, however, the waves that pass 



J^28 



ELEMENTARY LESSONS ON [chap. xiii. 



through the coherer M are infinitely small, but they 
suffice to close the local electric circuit of M, the relay 
R and the battery b^ which works an ink-marking 
register or Morse instrument. 

448. The Relay. — Art. 426. Fig. 176 represents in 
detail some of the minor devices at the receiving sta- 
tion. A is the connection with the secondary winding 
//in Fig. 175. A wave received passes through the 
coherer C to earth E, causing the filings to form a 
conductor, and thus closing the circuit of the powerful 
battery N through the relay R. The relay magnet 
attracts the armature L, making contact at e. At H 
in our figure there is no contact shown, but when the 
apparatus is at rest there is a contact, closing a second 
circuit, of battery N through armature V, the trembler 
magnet M and the bell B. When theie is a contact at 

^, this second circuit 
is closed, the trembler 
magnet M attracts 
armature V, thereby 
striking the bell B 
with T and at the 
same time breaking 
its own circuit at H, 
whereupon the spring 
S brings the armature 
V back into its origi- 
nal position, causing 



A 

/ 


c^=, 


Tp^ 


— titja 


::::i 


H ^^c>- 


Y 


\ 




^=j 


II "^ 




1 

« 






11 " " 





Fig. 176. 



T at the same moment to tap the coherer, thus 
decohering the filings, and putting the apparatus in 
readiness for the next wave. Instead of a bell this 
circuit, in actual service, actuates an ordinary Morse 
instrument. 

In the above description we have spoken of * Verti- 
cal wires'* serving to emit and to detect respectively 
the ether waves. They have also been called ''anten- 
nae," especially when consisting in a single wire or in 
two wires insulated from each other. These wires are 
carried about two hundred feet up in the air, by means 
of tall masts. They may consist, also, of a solid wire 
covered with an insulating substance and contained in 
a close-fitting tube. Another form of antennae has 



Chap, xiii.] ELECTRICITY AND MAGNETISM. 



429 



two concentric cylinders, separated by an air space. 

(See Fig. 177.) The two antennae may be considered 

as forming two sides of 

a static condenser, 

one side of which 

alternating charge 

imparted through 

induction coil of 

transmitting station. 

While Marconi's sys- 
tem is exclusively em- 
ployed in the United 
States and England, 
there are several others 
in use in other countries, 
among which the Slaby 
system may be men- 
tioned as the most prom- 
inent one. Fig. 177. 




430 ELEMENTARY LESSONS ON [chap. xiv. 



CHAPTER XIV. 

X-Rays. 

Lesson XLIII. — Vacuum and Cathode Rays. 

449. Electric Egg. — In our lesson on phenomena of 
discharge, pages 235 to 253, much has been said that 
applies here. The student will advantageously reread 
that lesson, especially Arts. 292-294. 

The electric spark between the two conductors of an 
electric machine is visible because of the particles of 
air which it passes; the length of the spark, its form 
and color depend very much on the density of the 
intervening air, as may be shown by means of an 
apparatus known as the electric egg. (See Fig. 150.) 
This is a strong, egg-shaped glass bulb with a stop- 
cock fixed at its lower end, and a brass rod cemented 
in at the upper end, air-tight but movable. The rod 
at the lower end is also cemented in and not movable. 
The lower end can be screwed air-tight to an air-pump, 
and the outer ends of the two brass rods are connected 
with the terminals of an electric machine. When the 
apparatus is emptied of air to a high degree, the elec- 
tricity generated by the electric machine streams from 
one knob to the other in broad bands of light. If 
more air is allowed to flow, little by little, back into 
the egg, the light bands grow more and more narrow, 
and approach the shape of a spark. The brilliancy 



CHAP. XIV.] ELECTRICITY AND MAGNETISM. 431 

and beauty of this phenomenon is greatly enhanced, if 
instead of an egg-shaped vessel, first used by Sir Wil- 
liam Crookes, a long glass tube is employed, first 
made by Geissler of Bonn. Such tubes are called 
Crookes tubes or Geissler tubes. 

450. Effect of Electric Current. — In the preceding 
paragraph we spoke of the effect of a charge of static 
electricity. A current of electricity from a battery 
has no such effect, at least not until it has been 
converted into an induced current. (Art. 393.) 
But if a Ruhmkorff induction coil is connected 
between the terminals of a Geissler vacuum tube, a 
very interesting spectacle may be observed. Fig. 
178 shows such a tube in action under an mduced cur- 
rent. At its two ends two short pieces of platinum 
wire are sealed in, the electrodes, which connect 
with the conductors outside. The + sign in the 
figure signifies the anode^ the - sign marks the cathode. 
When the tube is emptied of air until it contains 
only a five-hundredth part of the ordinary amount, 
the electric current causes the following phenomena: 
the cathode is enveloped in a sheath of pale bluish 
light, at the end of which towards the middle of 
the tube a gap occurs, while from the anode a pro- 
cession of beautiful purple striae, with dark spaces 
between, seems to move toward the cathode. This stria- 
tion is due to the action of the interrupter or break con- 
nected with the induction coil. As the air is exhausted 
more and more, the pale sheath of light draws away 
from the cathode, leaving a dark space inside, and 
finally dies away, and instead of the rarefied air within 
the tube giving light, a part of the glass itself begins to 
glow with a y^Wo-^ fluorescence or glow, the hue of which 
varies with the chemical composition of the glass. 

451. Radiant State. Cathode Rays. — Atmospheric air is 
a gas, and according to the kinetic theory "a gas con- 
sists of a large number of molecules moving with great 
velocity." The number of molecules in the smallest 
quantity of gas is so great, however, that one of them 
can move a very short distance only before it collides 
with another. But if the gas is rarefied, as air in a 
vacuum tube, this distance or free path becomes longer, 



432 ELEMENTARY LESSONS ON [chap. xiv. 

and when the vacuum is nearly perfect the few mole- 
cules remaining in the tube may fly from one end to 
the other without colliding with each other. In this 
condition a gas is said to be in the radiajit state. In a 
Crookes tube connected with an induction coil the 
cathode repels the remaining few molecules with 
great violence and in a straight line; and it is this 



Fig. 178. 

violent bombardment on the glass wall at the other end 
that seems to create the fluorescence. At least this is 
Crookes' theory. Other scientists, especially Lenard, 
have tried to prove this phenomenon to be some form 
of ethereal disturbance, terming it cathode rays, but 
Crookes appears to have substantiated his theory quite 
well by two experiments: one in which the flying 
molecules set a wheel of mica vanes into motion, 
and one in which a cross of mica in the tube inter- 
cepts part of the molecules so that the fluores- 
cence does not show where the intercepted molecules 
would have struck the glass, leaving a cross-shaped 
shadow, (See Fig. 179.) The question is an open 
one as yet. (See Art. 452.) The term ''cathode 
rays," being convenient, has been adopted univer- 
sally. 

452. Transparency to X-Rays. — Water and glass are 
transparent in the popular sense of the word, that light 
will pass through them. But in science the word has 
additional meanings; tor instance, ''glass is not trans- 
parent to heat-rays,'^ "a strong so'ution of iodine-, of 
very dark color, is opaque to light rays, but quite trans- 
parent to heat rays Rays of heat and light are transverse 



CHAP. XIV.] ELECTRICITY AND MAGNETISM. 



433 



vibrations of the ether, those of heat having a longer 
periodic time than those of light." (A transverse vibra- 
tion is exemplified by the vibrations of a violin string, 
whereas the air in a flute, when played upon, vibrates 
parallel to the axis of the air space in the instrument, 




Fig. 179. 



longitudinally, creating alternate compression and 
expansion of the air.) No longitudinal vibrations of 
the ether have been discovered, unless Prof. Roentgen 
is right in his suggestion that the X-rays may possibly 
consist in such ethereal motion. The cathode rays, he 
says, inpinging upon the glass wall of the tube, may 
cause a molecular change of position in the glass, 
which in turn may generate another form of motion, 
the X-rays, which pass, more or less, through the 
densest substances, and cannot be deviated by a mag- 
net, while the cathode rays can be so deviated. But 
this is anticipating somewhat. 

453. Peculiarities of Vacua. — We must treat of a few 
other phenomena first before we can turn to X-rays. 
When a Crookes tube is filled, not with air, but with 
some other gas highly rarefied, the color of the light 
in the tube varies, a circumstance of greatest value in 



434 



ELEMENTARY LESSONS ON [chap. xiv. 



spectral analysis. In rarefied atmospheric air some 
bodies become luminous, rubies show a red light, 
diamonds green, etc. Hittorf and Crookes discovered 
independently that when the vacuum in the tube is 
gradually increased to such a high degree that but one 
millionth part of the atmospheric air finally remains, 
the rW light recedes more and more with the increas- 
ing evacuation, 
.. j>^ / i\ R while the blue 

^^ '^ yiBwO light expands 

more and more 
and at last fills 
the whole tube. 
In a Crookes 
tube filled with at- 
mospheric air the 
induction spark 
will pass around 
corners and follow 
any bend of the 
tube, but the ca- 
thode rays extend 
in straight lines 
(See Art. 451, where the 
How- 




Fig. 180. 



only, generally speaking. 

rays are said to outline the shadow of a cross.) 

ever, when the electrodes are placed, not opposite 

each other, but at angles, as in Fig. 180, the sparks 

move in curves. 

In Fig. 180 A, the tube has an ordinary vacuum, 
while in B the vacuum is one of very high degree. In 
each case the negative pole of the induction coil is 
connected to N, the positive pole to one of the three 
P^s. N is connected with ^, the aluminium cathode, 
which is shaped like a concave mirror; the anodes, 
b, c^ d^ are common platinum wires. In A the sparks 
move in curves, according as the positive poles P are 
connected to ^, c or d^ while in B, no matter whether 
the positive pole is connected to b, c or d, the rays ex- 
tend straight from each point of the concave mirror, 
cross each other in a focus and strike the glass wall 
opposite, causing it to fluoresce. 

Lenard, a pupil of Hertz, found that these cathode 



CHAP. XIV.] ELECTRICITY AND MAGNETISM. 435 

rays can be made efficient outside of the tube. He 
cut a piece out of the glass wall, inserted a thin sheet 
of aluminium air-tight, and found that a photographic 
plate placed behind this aluminium window was black- 
ened as if by real light rays. 

Crookes found that the stream of cathode rays couid 
be deflected by a magnet. He had discovered that a 
phosphorescent screen placed lengthwise in the tube 
was lit up by the 
cathode rays, so that ^^^^. ^^^^^g— ^..........^^ 

the track of the mole- %Jj^y[_ ^ ■ — ^ -j^,;,;^^;^^ 

cules was easily traced. |l19 

Then he placed a mica IB 

plate with a small hole ^ ^g^ 

in the middle near the 

cathode, so that the stream had to pass through this 

hole. When a strong magnet was placed against the 

middle of the tube the phosphorescent streak was 

deflected strongly. (See Fig. 181.) 



Lesson XLIV. — X-Rays. 

454. Discovery of X-Rays. — Roentgen spoke of his 
discovery, made on Nov. 8, 1895, ^^ follows: *'I was 
working v/ith a Crookes tube covered by a shield or 
screen of black cardboard. A piece of barium platino- 
cyanide paper lay near by on the table. I had been 
passing a current through the tube and noticed a 
peculiar black line across the paper. As this effect 
could be produced by the passage of light only, and 
as no light except from the tube could have struck the 
plate, I made a test at once, and found that some kind 
of rays actually passed through the black cardboard 
cover. In a completely darkened room the paper 
screen washed on one side with barium platino- 
cyanide lighted up brilliantly, and fluoresced equally 
well no matter which of its sides was turned towards 
the tube. This fluorescence was noticeable even at a 
distance of two meters. The most remarkable thing 
to me was that this fluorescence passed through the 
black cardboard cover, which transmits none of the 



436 ELEMENTARY LESSONS ON [chap. xiv. 

ultra-violet rays of the sun or of the electric arc. I 
found by experiments that all bodies are transparent 
to this influence, although in very different de- 
grees.'' 

Because of these differing degrees of transparency 
opaque bodies throw a shadow, and for this reason 
Roentgen called this influence rays, and because their 
real nature is unknown he called them X-rays. 

455. Properties of X-Rays. — The transparency of 
different bodies for X-rays varies greatly. The rays 
pass through wood, paper, hard rubber with ease; the 
fluorescent screen lights up brightly behind a bound 
volume of looo pages, the printer's ink offering no 
perceptible obstacle. A single sheet of tinfoil hardly 
casts a shadow. Glass plates of the same thickness 
behave in different ways, according as they contain 
lead or not; the former are much more opaque than 
the latter. Animal bone is quite opaque. Blood is 
more opaque than flesh. Platinum 0.2 mm. thick is 
transparent; silver and copper sheets maybe decidedly 
thicker. Lead 1.5 mm. thick is practically opaque. 
In general, it may be said that the density or atomic 
weight of the substances determines their transpar- 
ency, but several exceptions to this rule have been 
established. 

Transparency increases with the hardness of the 
tube; with tubes of medium hardness the difference in 
transparency between the bones and the soft parts of 
the human body is greatest; therefore the radiographs 
of animal objects made with very soft or very hard 
tubes are of little or no value. 

One peculiar property is common to X-rays and to 
ultra-violet light rays: both cause a discharge of 
bodies that are electrically charged, but with this 
difference that they have this same effect upon both 
positive and negative charges, while ultra-violet light 
rays discharge negative charges only. 

456. Nature of X-Rays. — Some scientists have re- 
garded X-rays as light rays of very small wave length, 
but the sounder theory seems to be that they are 
instantaneous impulses produced by the impact of 
electrons upon the anti-cathode. They may be likened 



CHAP. XIV.] ELECTRICITY AND MAGNETISM. 437 

to the sound waves produced by rain drops on the 
roof» not of a definite pitch. The velocity of X-rays 
is probably the same as that of Hertzian waves. 

Lenard showed that a magnet defle<:ts cathode rays 
even outside the tube, while X-rays are uninfluenced 
by a magnet. This seems to show a great difference 
between the two, and would appear to exclude the 
possibility of their being identical. But the X-rays 
are by no means homogeneous, at least not in their 
effects. Those emitted by a low or soft (lightly 
exhausted) tube have very little penetrating power; 
the rays of a high ox hard (highly exhausted) tube have 
great penetration. Neither extreme is serviceable for 
practical X-ray work. A low tube requires a shorter 
spark to excite it than a high tube, and is therefore 
said to have a lower resistance. 

The question whether cathode rays are able to fur- 
nish photographs like X-rays is an open one. Prof. 
Slaby is said to have succeeded in photographing by 
this means through an aluminium window in a Crookes 
tube, and if this is correct, Lenard operated with 
X-rays before Roentgen; of course, without discover- 
ing the fact. 

457. Source of X-Rays. — The discharge of a high 
potential electric current is the only practicable source 
of X-rays, although Henri Becquerel in 1896 discov- 
ered that several chemical substances also had the 
property of affecting photographic plates through 
opaque wrappers. Mr. and Mrs. Curie of Paris have 
devoted much time to these radio-active substances, 
and have established radium as a distinct element. 
Two other radio-active elements have been discovered, 
polonium and actinium, while thorium and uranium 
appear to have some radio-active qualities. This 
newly-opened field seems to be full of unlimited and 
most interesting possibilities. 

458. X-Ray Apparatus. — The instruments needed for 
radiography are: a vacuum tube, a battery with 
Ruhmkorff induction coil and interrupter, and a pho- 
tographic plate. Of these we will now treat in detail, 
referring the reader to much that has been stated in 
other parts of this book. 



438 



ELEMENTARY LESSONS ON [chap. xiv. 



459. Focus Tubes. — In order to do good work the 
area of glass which emits the X-rays should be quite 

small. However, it 




Fig. 182. 



will not do to con- 
verge the rays from 
the cathode in a focus 
on the glass, because 
the glass would soon 
melt at that point, 
and the tube would 
be ruined. A modern 



focus bulb tube has a concave cathode, but the con- 
verging stream of molecules impinges on a platinum 
anode inclined at an angle of 45 degrees, a small 
spot on which then becomes the center, from which 
the X-rays are sent forth. (See Fig. 182.) The 
cathodes of focus tubes are invariably made of 
aluminium, because they are not liable to any 
change, while gold and platinum cathodes seem to 
volatilise, depositing a film on the glass of the tube 
where they are carried with the stream of molecules. 
This has a double disadvantage: the glass becomes 
more opaque to X-rays, and the film occludes (absorbs) 
particles of air, thus increasing the vacuum, that is, 
changing a soft tube into a hard one. 

A bulb tube should always be heated during the pro- 
cess of exhausting, because the inner surface of the glass 




Fig. 183. 



has a condensing action on the air, preventing its 
thorough removal by the pump. This condensation is 
overcome by the heat. A very modern tube is the 
one shown in Fig. 183. It is a biaTwdic double bulb 



CHAP. XIV.] ELECTRICITY AND MAGNETISM. 439 

focus tube. The subsidiary bulb gives an increased 
volume to the tube, and acts as a. kind of reservoir. 
The subsidiary anode enables the tube to take a larger 
current without injury. It is possible to regenerate 
the vacuum in this tube, when its resistance has 
become too high. The two anodes are disconnected, 
the aluminium anode is connected to the negative 
terminal of the induction coil, and the cup-shaped 
cathode to the positive terminal. By passing the 
spark in this way for some time, the resistance can be 
considerably lowered. 

460. Adjustable Tubes. — In order to be able to use the 
same tube for X-rays of the highest and the lowest 
penetrative power, and all intermediate values, the 
cathode, placed in a conical annex, is mounted upon 
a steel rod, held in guides, so that by gentle tapping 
against the glass it can be moved a little, about one- 
half of an inch. Where the cathode is farthest from 
the anti-cathode, its edge is very near the glass all 
around. This annular space between the cathode 
edge and the glass becomes larger and larger as the 
cathode is moved nearer the anti-cathode. Where the 
cathode is nearest to the anti-cathode it is no longer 
in the annex, but has just emerged into the principal 
bulb. 

461. Toepler's Pump. — There are four varieties of 
pumps used to exhaust the air from a tube: the old 
mechanical form, of little use for obtaining high 
vacua; the water-exhaust pump, intended mostly as an 
auxiliary to a mercury pump; the oil pump; and the 
mercury pump. Of the various mercury pumps we 
will describe Toepler's pump, of which the most mod- 
ern apparatus is a rather complicated application. In 
Fig. 184 A is a glass reservoir, into which mercury is 
poured to run down through the flexible rubber tube B 
and to rise again in the glass tube C. C opens into 
the reservoir D and into tube E, which again opens 
into tube F, and also into the tube leading from D 
upward and then down into the 'open reservoir M. 
The X-ray tube to be exhausted is sealed to the open 
end of F. As the mercury poured into A rises in 
C, D and E, it drives the air contained in the parts 



440 



ELEMENTARY LESSONS ON [chap. xiv. 



out through M. Finally the mercury itself will run 
down into the reservoir M, from which it, is dipped 
out, to be poured back into A. When the mercury 
has begun to run into M the reservoir A is lifted from 

its base and is lowered until 
most of the mercury has 
flowed back into it, and the 
air contained in the X-ray 
tube has distributed itself 
throughout the tubes. Then 
A is placed on its base 
again, the mercury drives out 
again a quantity of air in 
the way described, and this 
process is repeated until the 
desired vacuum is estab- 
lished, when the tube is 
sealed off from tube F. The 
mercury in M prevents the 
air from reentering the sys- 
tem of tubes. The mercury 
must be carefully guarded 
from dust, dirt and moisture. 
462. The Induction CoiL— 
A thick wire capable of 
carrying a large current is 
wrapped in a coil around a 
bundle of soft wires. Out- 
side this, and carefully 
insulated from it, is a coil 
consisting of many turns of 
fine wire, each turn well in- 
sulated from the next. The 
coil of thick wire forms the 
primary, and the coil of 
thin wire the secondary 
circuit. (See Art. 398.) In 
mechanical arrangement for 




Fig. 184. 



the primary circuit is 

rapidly making and breaking th^ circuit, a simple form 
of which has been described on page 369. Of these 
breaks or interrupters many ingenious types have been 
invented, among which those using a contact of mer- 



CHAP. XIV.] ELECTRICITY AND MAGNETISM. 441 

cury and a platinum wire seem to be the most service- 
able to date. In Tuaking, a current rushes through 
each loop of the primary wire, inducing momentary 
opposite currents in the next loop of the primary wire 
on either side. This will oppose and therefore retard 
the original current, but it lasts but a moment and 
does not stop the battery current; it merely causes it 
to reach its maximum value gradually (self-induction). 
In breaking, a self-induced current tends to pass along 
in the direction originally taken by the battery cur- 
rent, and, being of high E. M. F. , is apt to spark 
across the contact breaker. As such sparking would 
cause the break to take place slowly or not at all, the 
condenser is introduced, which acts as an electrical 
cushion, absorbing the shock of the self-induced cur- 
rent, and giving it back again to slacken the strength 
of the make in the primary. The total effect is a 
gradual make and a sudden break. 

463. Plate and Exposure. — Radiography, or photog- 
rapy by the use of X-rays, is to be distinguished from 
radioscopy, in which the screen discloses the image 
to the human eye directly. The latter is quicker 
work, but the photographic plate gives better defined, 
more detailed results, and gives a permanent record. 
An image which, when thrown on a screen, is not per- 
ceptible, can be registered on a plate by merely pro- 
longing exposure, as the effect of the rays on a plate 
is cumulative. 

The methods of photographing apply also, in gen- 
eral, to radiographing. A few exceptions and peculi- 
arities will be noted here. Either dry plates or films 
may be used. A fast plate gives more satisfactory 
results than a slow one. A very rapid kind of bro- 
mide paper is termed X-ray paper, as many experi- 
menters prefer it for radiographing. 

The object must be placed between the vacuum tube 
and the plate. Since it is essential that the object to 
be radiographed should be as close as possible to the 
plate, the thinnest covering should be used for the 
plate that will keep out the light, as a black envelope. 
Great care must be taken to remember which side of 
the plate is the sensitive one, as a reversed image 



442 ELEMENTARY LESSONS ON [chap. xiv. 

might lead to grave errors. It is recommended to 
form the habit of placing the sensitive surface in con- 
tact with the seamless side of the envelope. Unex- 
posed plates in their envelopes should not be brought 
near a working X-ray apparatus, except in a lead box, 
which would effectually protect them from the rays. 
The vacuum tube should be not too far from nor too 
near to the plate, because the shadows become dis- 
torted at improper distances; for instance, a circular 
object like a coin throws an elliotical shadow unless 
the rays strike its surface perpendicularly. Another 
reason is, that the power of the rays varies inversely 
as the square of the distance of the tube from the 
plate or screen. Of course a longer exposure would 
make up for a greater distance, but during a long 
exposure the X-rays produce in more or less opaque 
substances secondary rays which interfere with the 
work of the primary rays, causing a blurring of the 
shadows. It is evident that in radiographing a thin 
object, like a hand, the distance between tube and plate 
can be much less than in radiographing the chest. In 
the latter case the distance must be large enough to 
avoid distortion, that is to say, to get a radiogram of the 
same length and width as the object, as far as possible. 

It is usual to heat the tube during radiographing, 
with the advantage that tubes which have grown hard 
by continual use can be used hot after their resistance 
has become too great for the coil used. 

One of the greatest difficulties of the radiographer 
is to arrange his exposures so as to differentiate 
between different substances, all transparent but in 
varying degrees. The other chief factors in determin- 
ing the proper time of exposure are: the size and 
efficiency of the coil, the current used in the primary 
coil, the distance of the tube, and its resistance. The 
sparks between the two terminals of the coil should 
pass with a sharp snap and at short intervals for radio- 
graphy, while for screen work a steady flow is neces- 
sary. The current in the primary is gauged as to 
strength by the voltmeter, while the ammeter is used 
to insure an accurate repetition at will of the electrical 
condition necessary for making exposures. 



CHAP. XIV.] ELECTRICITY AND MAGNETISM. 443 

A soft tube enables the worker to take a radiogram 
without much regard to the time of exposure, as 
scarcely any rays will penetrate the more opaque parts 
of the hand, for instance. But a hard tube, although it 
gives a poor image, with faint shadows on the screen, 
gives also a very good image on the plate, because the 
rays lose their photographic power to a large extent 
on passing through opaque substances and it takes 
some time before the cumulative action of these rays 
acts on the plate. Thus a rather hard tube lessens the 
time of exposure. 

464. Time of Exposure. — Generally speaking, with the 
coils most in use having 6 to 10 inches spark length, 
exposures of from 20 seconds to a minute, according 
to circumstances, may be used. With a 20-inch coil 
and a mercury break, one flash (one make and break) 
will give the outline of the bones; 20 flashes will give 
an excellent radiogram. An arm requires from one 
minute in a child to four minutes in an average-sized 
man. The congenital hip dislocation shown in the 
frontispiece is after a radiogram which was exposed 
two and a half minutes, using a 12-inch spark. 

465. Uses of X-Rays. — Both science and industry 
were immensely interested when Prof. Roentgen pro- 
claimed his discovery. The possibilities of the new 
agens aroused great hopes for new knowledge in 
innumerable ways, and the most sanguine expectations 
have not been disappointed, except in a few instances. 
In metallurgy great strides have been made by means 
of radiograms in the knowledge of the structure of 
metals and especially of alloys, which were proved to 
go through a series of changes, when allowed to cool 
and solidify slowly, similar to those which take place 
when aqueous solutions of various concentrations are 
slowly cooled down below the freezing point. \x\ jew- 
elry, the real precious stones are readily passed through 
by the X-rays, while their imitations are much less 
transparent. On the other hand, a real pearl is quite 
opaque, while an artificial one is generally made cf a 
bulb of thin opalescent glass, coated internally with a 
preparation made from fish scales and filled with wax, 
and is therefore more transparent than the genuine 



444 ELEMENTARY LESSONS ON [chap. xiv. 

article. The greatest benefit from X-rays has been 
derived by the science of medicine and surgery^ as by 
their use the nature as well as the extent of an injury 
in the body, the presence of foreign substances, and 
their exact position, and also the condition of diseased 
parts in many cases, can be determined quickly and 
accurately. A case in point is a fracture involving 
one or more bones at or near a joint. Such a fracture 
is frequently, even by the best surgeons, mistaken for 
a sprain, especially at the wrist, shoulder, elbow or 
ankle. In each of these cases the X-rays have demon- 
strated fractures that formerly were not even sus- 
pected. Congenital luxations (hip dislocations exist- 
ing at or dating from birth; see frontispiece), so 
successfully treated by Dr. Lorenz of Vienna, are 
generally not recognized until the child begins to 
walk, but by this time the tendons and muscles have 
adapted themselves to the changed position of the 
thigh bone, and a false articulation has been formed. 
A cure requires an operation of considerable extent, 
and operative skill of high degree, while a compara- 
tively simple process would suffice if applied in time. 
A radiogram of a baby^s hips will show a luxation very 
plainly. Foreign bodies, as bullets, needles, etc., can 
be readily located in a body, either by taking pictures 
stereoscopically, and looking at the negatives in a 
reflecting stereoscope, or by taking two pictures of the 
same part from two sides ninety degrees apart. The 
diagnosis of calculi or stones in the kidneys, so diffi- 
cult to recognise by ordinary methods, is made a mat- 
ter of comparative simplicity by the X-rays. The 
same is true of stones in the bladder. In dentistry the 
process of dentition may be studied by the use of 
X-rays much more fully and satisfactorily than before, 
the structure of an individual tooth may be recog- 
nised, and abscess cavities can be positively located. 
Some diseases, as cancer, seem to be curable by 
exposure to X-rays, but the experiments in this line 
have not yet been ample and varied enough to allow 
of final conclusions. So much is certain, that the rays 
have a decided influence on the tissues of the human 
body, but it remains to be learned how to control this 



CHAP. XIV.] ELECTRICITY AND MAGNETISM. 445 

influence for the benefit of the suffering individual. 
After repeated short exposures of a part of the body 
to the energy emanating from a vacuum tube, peculiar 
secondary effects have manifested themselves, varying 
from a slight reddening of the skin to a deep burn or 
ulcer. 



440 ELEMENTARY LESSONS ON [chap. xv. 



CHAPTER XV. 

Central Station. Modern Dynamos and Motors. 

Lesson XLV. — The Central Station, 

466. — The various central stations in use may con- 
veniently be classified as follows: 

1. Low pressure continuous current stations with or 
without secondary batteries. 

2. Medium pressure continuous curreut stations. 

3. High pressure alternate current stations. 

In the first class mentioned, according to the Board 
of Trade regulations, the pressure does not exceed 300 
volts for continuous, or 150 volts for alternate cur- 
rents. The second class employs pressures from 300 
to 800 volts. Systems using high voltages, up to 3000 
volts, are termed **high pressure supply systems,^ 'and 
those in which the pressure exceeds 3000 volts are 
called **extra high pressure systems." 

467. Transformation. — We have seen that the rate at 
which an electric current does work is given by the 
equation 

W = E C watts, 

where W represents the work done, E the electromo- 
tive force in volts, and C the magnitude of the current 
in volts. This equation, being true for the whole cir- 
cuit, is true for any part of it. Therefore the work 
(w) done per second by the current (C) between two 
points whose potential difference is e^ is given by the 
equation 

w ^ e Q watts. 



CHAP. XV.] ELECTRICITY AND MAGNETISM. 447 

The problem is to make this quantity w as large as 
required at the distant point, and at the least possible 
expense. According to Joule's law the loss by con- 
version into heat is = C2R (see Art. 367), and thus we 
have 

z«; = W-C2R. 

The smaller the subtrahend C2R, the larger will be 
w. R may be diminished by increasing the cross- 
section of the conductors, which, however, involves a 
great expense. C may be diminished at will, and 
without diminishing the value of E C = W if we pro- 
portionally increase E. If C is diminished tenfold, 
and E is increased tenfold, W will remain unaltered, 
while C2R is reduced to a one-hundredth part of what 
it was before, or a conductor of a one-hundredth of the 
cross-section will be available. This system gives a 
small current of great potential difference. If the cen- 
tral station supplies motors only, all that remains to be 
done is to wind the motors with fine wires and care- 
fully insulate them. But where the power is to be used 
for general purposes, and especially where electrical 
energy is to be supplied to private houses, it is not 
admissible to leave the control over a high potential 
difference to the consumers. In such cases a trans- 
former must be interposed to change the pressure. 

468. Low Pressure Systems. — In these the electrical 
energy is supplied direct to the consumers at the 
pressure at which it is generated. Secondary batteries 
are frequently used as equalisers of pressure or as 
storers of energy for relieving the engines at the 
periods of heaviest demand, and often for taking up 
the whole of the supply during the hours when the 
demand is lightest. 

The conductors are divided I'aX.o feeders, which sup- 
ply the current from the central station to the dis- 
tributors at definite points, and the distributors, to 
which the consumer's wires are directly attached. 
The distributors consist of either two or three wires 
(see Art. 472), to which the consumer's wires are 
joined in simple parallel. From the points where the 
distributors take the current from the feeders, thin 



U8 ELEMENTARY LESSONS ON [chap. xv. 

insulated *'pilot'' wires lead to the station. These, 
when connected to the voltmeters on the switchboard, 
enable the attendant to ascertain the potential differ- 
ences at the feeding points, so he may take steps to 
keep the pressure constant. 

From each dynamo in a low pressure station posi- 
tive and negative conductors lead to the switchboard, 
where by suitable switches they can be placed in con- 
nection with a pair of heavy copper bars, called 
omnibus or bits bars. One of these leads from each 
dynamo passes through an ammeter which indicates 
the current which the particular dynamo is supplying 
at any moment. The ends of the feeders are also 
brought to the switchboard, the negative feeders being 
directly connected to the negative bus bar through a 
safety cut-out. The positive feeder leads through an 
ammeter to a regulating switch, by means of which a 
secondary battery can be switched in or out, entirely 
or graduall}^ 

469. Medium Pressure Systems. — In these systems, 
with a pressure from 300 to 800 volts, distribution is 
effected either by means of a further development of 
the three-wire system, known as the five-wire system, 
or by means of a step-down transformer. The five- 
wire system (see Art. 472) has five distributors, num- 
bers I and 5 having a potential difference of four times 
that between any contiguous pair. Each consumer is 
connected to two contiguous mains only out of the 
five, so that he gets only one-fourth of the pressure. 
In order to keep the potential difference of the various 
pairs of wires constant, in spite of the uneven con- 
sumption by the consumers, the pressure is auto- 
matically regulated by secondary batteries, or, in the 
case of serious variations, by a special commutator 
automatically worked by a motor dy?iamo. A motor 
dynamo or **electric motor" is a reversed dynamo 
supplied with energy in the form of an electric cur- 
rent at a high potential. It will rotate and will drive 
a low pressure continuous current dynamo, thus trans- 
forming a small current at high pressure into a large 
current at low pressure. The two machines are made 
into one by having one set of field magnets, and one 



CHAP. XV.] ELECTRICITY AND MAGNETISM. 449 



armature wound with two entirely distinct circuits 
provided with separate commutators. 

470. High Pressure Systems. — These use pressures of 
1000 volts and upwards, and for the transmission of 
energy usually employ alternate currents, readily 
'^transformed'' into currents at a lower pressure by 
means of induction coils, now generally termed 
"alternate current transformers.'' These work with a 
loss that even at full load amounts to less than 5 per 
cent. The primaries of all the transformers are all 
arranged in parallel on a pair of mains as in the two- 
wire system. Frequently there are two sets of trans- 
formers, especially where small dynamos are used; one 
set transforms the energy '*up" to a less current at 
higher voltage, and the second set transforms it 
"down" to the voltage required by the consumers. 

471. The Switchboard. — The general rule should be 
so to place the switchboard that it is very accessible 
and may be watched simultaneously with the dynamos. 
Marble is the best material, because of its fine insulat- 
ing properties. The switches may be mounted on the 
marble without separate bases. The equipment for 
each individual generator is usually mounted on a 
single panel, except for very large work. Where a 
generator or transformer gives from 5000 to 12,000 
volts, the danger of arcing across at the switch is very 
great, and the gaps must be of corresponding width. 
Where step-up transformers are used in a plant, the 
switches are best placed on the low voltage side, so as 
not to be obliged to interfere at all with the high ten- 
sion lines when carrying current. The result of a 
short circuit is often a fierce arcing, which must be 
provided against. Magnetic cut-outs are preferable to 
fuses, but where fuses are used, a few close-fitting 
large asbestos-paper washers should be strung along 
them to break the arc, and the fuses should be far 
enough apart to prevent the arc cutting over from line 
to line. Ammeters and voltmeters should be of the 
best quality and accurately adjusted. They should 
have large dials. 

Every station should have a traveling crane, able to 
lift and move any weight likely to need moving. 



450 



ELEMENTARY LESSONS ON [chap. xv. 



472. Three-wire System. — This invention of Edison 
includes three main wires. Where dynamos are used, 
they are arranged in groups of two. One lateral lead 
starts from the negative bmding post of one dynamo, 
the positive terminal of which connects to the nega- 
tive of the other. Between the two dynamos the 
neutral third wire is connected. The other lateral lead 
starts from the positive binding post of the second 
dynamo. (See Fig. 185, which shows the diagram of 
a lamp circuit.) The lamps are calculated for the 
potential difference of a single dynamo, and are dis- 
tributed evenly on both sides of the neutral wire. 
When the distribution is exactly even and all the 
lamps are burning, no current flows through the neutral 
wire. If all the lamps on one side are out, the cur- 



QO99669O 











L. 



m 



T+ 



Fig. 185. 

rent goes through the neutral wire instead of the lateral 
on that side. In other cases, when one or more lamps 
on one side are out, the neutral wire carries the excess 
of current. In this system smaller wire can be used 
for the same voltage than in the two-wire system. 
The four-wire and five-wire systems are applications of 
the three-wire system. They use three and four dyna- 
mos respectively, or one dynamo with special armature 
connections to give the requisite three-fold or four- 
fold division of total potential. 

The three-wire system is also used for distribution of 
power to railway and other motors, allowing a trans- 
mission of 1000 volts and the employment of looo-volt 
motors, and at the same time using motors of all sizes, 
if only it is possible to fairly balance the two sides. 



CHAP. XV.] ELECTRICITY AND MAGNETISM. 451 



Lesson XLVI.^ — Modern Dynamos and Motors, 

473. Dynamo and Motor. — A dynamo is a generator 
of electrical current; that is, a machine for converting 
mechanical energy into the energy of electric currents. 
An electric motor does mechanical work at the expense 
of electric energy. Any kind of dynamo, whether 
for continuous or alternating currents, can be used con- 
versely as a motor, though some more appropriately 
than others. Numerous attempts were made between 
1823 and 1840 to invent a motor that could be used 
commercially, but in vain, since at that time there was 
no economical method known of generating electric 
currents, and the great physical law of the conservation 
of energy was not recognised, and its close bearing 
upon electric machinery was not anticipated. 

The one great difference between a generator and a 
motor is, that in a generator the brushes have a for- 
ward lead, while in a motor, in order to minimise 
sparking, the brushes must be set back, or given a 
backward lead. In a motor greater care must be taken 
with the lamination of the iron of the magnetic circuit 
in order to avoid eddy currents; also special attention 
must be paid to the mechanical arrangements transmit- 
ting the magnetic drag in the wires to the shaft. 

474. Propelling Drag and Counter Electromotive Force. 
— The rotation of a motor is due to the propelling 
drag. The drag which the magnetic field exerts upon 
the armature wires through which the current is flow- 
ing is the real driving force which propels the revolv- 
ing armature. In a generator the drag acts in a 
direction which opposes the rotation. The difference 
between the power furnished to the motor and the 
work done by it is due to the fact, discovered by 
Jacobi in 1835, ^^at the motor by the act of revolving 
begins to work as a dynamo, setting up a current in the 
opposite direction to that which drives it. The faster 
it rotates the greater is this counter electromotive force. 
(See Art. 377.) This is a precisely parallel case to 
that of attaining the maximum current of a battery by 
so grouping it that the internal resistance of the bat- 
tery shall, as nearly as possible, equal the external 



452 ELEMENTARY LESSONS ON [chap. xv. 

resistance, (See Art. 351.) This rule is true for 
maximum current and for maximum rate of using up 
zinc; but it is by no means a rule of greatest economy. 
For economy the internal resistance should be much 
less than the external, but not so much less as to 
reduce the current too much. Similarly, the resist- 
ance of the motor armature should be very low as 
compared with that of the external circuit. Both 
cases, motor and battery, are applications of the old 
rule that a machine (or a man or beast of burden, for 
that matter) does not generally do its work with the 
greatest economy, when it performs the largest 
amount of work in the shortest possible time. 

475. Torque. — The force necessary or tending to 
produce torsion (turning) around an axis is called 
torque. It is used especially of the pulling ox turning 
moment of an armature of an electric motor upon its 

__ ___,^ shaft. The torque of a 

^"^^^^^V motor is equal to the pro- 

^^^^^^^^> ^ duct of two factors, namely, 

^s^-z^^?^5 the pull exerted at the ar- 

t~^^^d___ i^ature periphery, and the 
""" ^^^««««M>-- armature radius. When the 
^^^eaae^^ — . pull is measured in pounds 

^^' '^^' ^ and the radius in feet, the 

torque is expressed in pound-feet. In metric units the 
pull is usually measured either in kilogrammes and 
the radius in meters or centimeters, and the torque is 
then expressed in meter-kilogrammes or centimeter- 
kilogrammes. 

Motors should be designed with a view not only to 
working with a constant electromotive force supplied 
at the electric mains, but also to working at uniform 
speed, whether the work be light or heavy, or whether 
the machine run idle. 

476. Alternate Currents. — Fig. 186 shows a single 
loop of wire arranged to turn continuously in the 
space between the poles of an electromagnet, a region 
of great electromagnetic stress. The two ends of the 
loop are connected to two insulated metal rings con- 
nected by brushes to an external circuit. In the 
vertical position shown the loop is under the full influ- 




Fig. li 



CHAP. XV.] ELECTRICITY AND MAGNETISM. 453 



ence of the magnetism. If the loop were in a hori- 
zontal position, the magnetic influence upon it would 
be very much smaller, because only the force emanat- 
ing from a narrow strip of the N pole of the magnet 
would act upon the loop, on its way to the S pole. 
Now, whenever the elec- 
tromagnetic stress about 
a conductor changes in 
Tnagnittide (or, in other 
terms, when a conduc- 
tor cuts the lines of 
magnetic force), an 
electromotive force is set up i?i the conductor. This electro- 
motive force is, of course, proportional to the rate of 
change in the electromagnetic stress, which is largest 
when the loop is near the vertical position and = zero at 
the moment of horizontal position. The rise and fall 
for each full revolution (3600) of the loop is graphically 
shown in Fig. 187, being at a maximum at 90 and at 
270 degrees, the position shown in Fig. 188, where 
the loop stands at right angles to the lines of force. 
This wave is called the sine wave^ because the electro- 
motive forces set up are proportional to the sine of the 
angle through which the coil has turned from the posi- 
tion in which it lay across the field. 

During each whole revolution of 360 degrees there 
are two waves in opposite directions. In a continuous 
current machine these two currents of electricity are 
made to flow in the same direction by the commutator, 
but in alternate-current machines two slip rings take 
off the current. Each complete revolution consists of 
two periods, and the number of periods in a second is 
called the frequency or periodicity of the alternations. 
In multipolar machines this number is greater than in 
two = pole machines in proportion to the number of 
pairs of poles. 

477. Lag and Lead. — Alternating currents usually do 
not keep step with the alternating volts impressed 
upon the circuit. The currents will lag behind the 
voltage if there is inductance in the circuit, while they 
will lead if there is capacity in the circuit. This 
means that the impulses of current will occur a little 




454 ELEMENTARY LESSONS ON [chap. xv. 

later or earlier than those of the volts. These differ- 
ences in phase can be made to neutralise each other. 
The value by which, in the case of lag, the electromo- 
tive force must be divided to get the current, is called 
the impedance. A lagging current will also not rise to 
the same height as if it were not lagging, so that the 

actual wave will be 
like the heavy line in 
Fig. i88, in which the 
ideal wave is shown 
in a dotted line. The 
^^s-i^^' current is choked 

down, as it were. Impedance coils or choking coils 
is a term for self-induction coils with large in- 
ductance and small resistance. If the amperes 
and volts of an alternate current supplied to a 
motor are measured separately by ammeter and volt- 
meter, and the readings multiplied together, the prod- 
uct will exceed the true watts because of the difference 
in phase, of which the measuring instruments take no 
account. Therefore an electro dynamometer is used, 
so constructed that the high resistance circuit in it is 
non-inductive. 

478. High Frequency Currents. — The described effects 
of inductance and capacity increase with the fre- 
quency. With a frequency of looo per second the 
current does not flow equally through the entire cross- 
section of the wire, but is confined to the surface. 
The frequency of the oscillations in a discharge of a 
Leyden jar (see Art. 443) is so high that a hollow tube 
will conduct the current just as well as a solid wire, 
and this fact is the strongest ground for the modern 
theory that the energy in an electric circuit is trans- 
mitted by the surrounding medium, while the wire 
itself serves only as a guide. 

479. Alternators. — Alternate current machines gener- 
ally have a frequency from 50 to 120 per second, and 
generate a pressure from 1000 to 5000 volts. They are 
mostly multipolar, and because perfect insulation of 
the armatures is more easily obtained when they are 
stationary, the field magnet is made to rotate. Two 
or more continuous current dynamos may be coupled 



CHAP. XV.] ELECTRICITY AND MAGNETISM. 455 

together without any difficulty, if they are run at the 
same speed and voltage; but two alternators joined in 
series must also be in phase With each other. Other- 
wise one will have at some moment a higher voltage 
than the other and will instantly send a current 
through it in the opposite way, tending to stop it and 
then to run it as a motor. If running in parallel this 
matter will correct itself, as the machine which leads^ 
or is a little ahead of the other, will have a larger 
load, tending to run the lagging machine as a motor, 
and in this way the latter is brought up so as to come 
back into phase. Thus two alternators will run well 
together in parallel, even when their E. M. F.'s are 
unequal, but when an alternator is to be switched into 
circuit, it is better to make sure first that speed and 
volts are proper, and then by means of the synchroniser 





Fig. 190. 

to ascertain that the alternator is in phase with the 
circuit before the switch is turned. 

A maphine which has a simple rotating armature and 
both a split-tube commutator to collect continuous 
currents, and a pair of slip rings for alternating cur- 
rents, may be used as a transformer, converting either 
kind of current into the other, or it may act as a motor 
if supplied with either kind of current, or if run by an 
engine may generate both kinds of current at the same 
time. 

480. Polyphase^Currents. — If two separate sets of coils 
are placed on the armature of an alternator, one 
a little ahead of the other (see Fig. 189), it is possible 



456 ELEMENTARY LESSONS ON [chap. xv. ^ 

to obtain two alternate currents of equal frequency 
and strength, but differing in phase by any desired 
angle or degree, generally by oiie-quarter of a period, 
and in this case if both currents are set to work they 
will combine to produce a rotary magnetic field, 
though the coil itself stands still. This is called a 
di'phase system of currents. A iri-phase system of cur- 
rents is created by having three coils and three alter- 
nate currents differing from each other by 120 degrees. 
(See Fig. 190.) Here the current first enters through 
the first coil and leaves through the other two, then it 
enters through the second and leaves through the first 
and third, and so on. The six-phase system consists 
of two three-phase systems in opposition to each 
other. In all these rotating magnetic fields masses of 
metal at once begin to rotate. The rotor generally 
consists of a cylindrical core built up of thin iron 
discs. It has no commutator or slip rings, receiving 
its currents wholly by induction. These asynchronous 
motors start with a great deal of torque and have a 
high efficiency in full load. ^ 

481. Classes of Dynamos. — According to the various 
modes of exciting the field magnets, dynamos are 
classified as follows: 

1. Magneto machine^ with permanent steel magnet. 

2. Separately-excited dynamo^ to which a separate 
machine, the exciter, furnishes the current used to 
excite the field magnet. 

3. Separate coil dynamo, in which a special coil 
wound on the armature generates the exciting current. 

4. Series wound dynamo, in which the few thick wire 
coils of the field magnet are in series with the arma- 
ture coils and the external circuit (Fig. 191). 

5. Shu7it wound dynamo, wherein the thin wire coils 
of the field magnet form a shunt to the main circuit, 
thus taking only a fraction of the current (Fig. 
192). 

6. Compound wound dynamo^ a combination of the 
series wound and the shunt wound system (Fig. 

193). 

In a series wound generator the volts rise as the cur- 
rent in the field coils is increased, because of the 



CHAP. XV ] ELECTRICITY AND MAGNETISM. 



457 



increase of magnetisation, but when this is near satura- 
tion they fall again because of internal resistance and 
reaction. When this resistance exceeds a certain value, 
depending in each machine on its construction, the 
machine will cease to yield any current when run at a 
given speed. 

A shu7it zvound dynamo has the peculiarity that in its 
two branches the current is inversely proportional to 




:^"^= 


J, 






Fig. 191. 



Fig. 192 



Fig. 193. 



the resistance in the branches (see Art. 353). Conse- 
quently, when the resistance in the outer circuit is 
increased, as by inserting a lamp, the current in the 
magnet coil will be increased, thus affording a kind of 
current self-regulation. On the other hand, the volt- 
age falls as the current increases, due to internal resist- 
ance and armature reactions. A rheostat is therefore 
inserted in the shunt circuit to regulate the electromo- 
tive force. 

The two systems just described have opposite faults; 
with series wound dynamos a small number of lamps 
can hardly be made to burn; with shunt dynamos the 
same number of lamps are in danger of being burnt 
out. Therefore a middle course between the two has 
been adopted: the compound generator, which may 
be regarded as consisting of a series dynamo machine 
with a shunted auxiliary machine. In Fig. 193 the 
thick wire is series wound, while the thin wire is 
shunt wound. Such a machine regulates the current 
without any further apparatus, and works uniformly 
with a varying resistance in the outer circuit. 

The Brush dynamo, known as an arc - lighting mdichm^^ 



458 ELEMENTARY LESSONS ON [chap. xv. 

regulates the output by shunting the exciting current; 
the Thomson-Houston machine effects the same pur- 
pose by automatically shifting the brushes. Both 
machines keep the current at lO amperes, while the 
E. M. F. changes from 50 to 2000 or more volts 
according to the number of lamps in circuit. 

482. Modern Motors. — There are two classes, those 
using continuous currents and those meant for alter- 
nating currents. The former have fixed field magnets 
and rotating armature, while the latter have the oppo- 
site arrangement. Since Jacobi, in 1850, discovered 
the fact that a dynamo may be run as a motor, the 
number of industries in which the electric motor has 
rivaled and superseded the steam engine, has grown so 
rapidly that we meet it everywhere, and there are so 
many types that it is impossible to describe them all. 
They are used on railways, in telpherage, for hoisting 
machines and elevators and in machine shops and 
small work shops for almost any purpose. We will 
describe here two types of stationary and one of rail- 
way motors. 

483. Thomson-Houston Stationary Motor. — A 15-horse- 
power motor of this type has an average efficiency of 
91 per cent at full load, obtained by a careful propor- 
tioning of the electric and magnetic parts. The mag- 
netic circuit is very short but of ample cross-section, 
and therefore of low resistance, and the magnetic 
poles are so formed and placed as to convey the 
magnetism into the armature with the least possible 
loss. The poles project upward, enclosing the arma- 
ture, which is nearly square in longitudinal section, 
consequently very short and relatively large in diam- 
eter. This gives a high peripheral velocity and a 
rapid cutting of the lines of stress. The field is wound 
in shunt to the armature and is relatively of a very 
high resistance. This reduces the amount of energy 
required to energise the field magnet to a very small 
fraction of the *total energy absorbed by the motor. 
The armature winding is of low resistance. The wire 
is held firmly in place by means of bands, so that they 
cannot yield to the centrifugal force even when rotat- 
ing at abnormal speed. 



CHAP. XV.] ELECTRICITY AND MAGNETISM. 459 

484. Tesla Polyphase Motor. — A 5-horsepower machine 
of this make has a rotary field made up of two distinct 
electrical circuits. The currents traversing these cir- 
cuits differ in their phases in such a way that one cur- 
rent is at its maximum when the other is at zero, the 
result being a rotation of the magnetism of the field. 
The armature is short-circuited, and the currents 
traversing it are simply the low potential currents 
induced by the field. As the insulation of the arma- 
ture is never exposed to a potential of more than a few 
volts, the armature cannot burn out. On the other 
hand, the field is so well insulated that it may be 
placed in a high potential circuit without the interpo- 
sition of step-down transformers. Neither commutator 
nor collecting rings are used. The coils of both field 
and armature are entirely concealed and protected 
from mechanical injury. The starting motors used 
with the two-wire synchronous system are of this type, 
the required difference of phase being obtained by a 
proper winding of the field circuits. 

485. Railway Motors. — Those most generally in use 
in street railways are of the ironclad type, completely 
protected from rain and water splashing from puddles. 
The armature is about 20 inches in diameter with a 
6-inch face, having 64 grooves with 14 windings of 
thick wire in each. At one end the armature shaft 
carries a pinion whose teeth gear into a larger wheel 
on the axle of the running wheels. Both are enclosed 
in a dust and vx^ater-proof case partly filled with heavy 
lubricating oil. The brushes are made of carbon, and 
fixed in stationary brushholders clamped in slots on 
each side of the bearing at the commutator end, and 
which can be quickly removed. They allow the arma- 
ture to rotate in either direction. The field magnet 
consists of two rounded shell-shaped iron castings 
hinged together at the back or axle end, and firmly 
clamped up, when in use, by four steel bolts. These 
shells serve as protection for the whole. The upper 
shell has a large pole piece, the lower has a small one; 
by this arrangement the armature is acted upon with a 
lifting pull which decreases the weight of the armature 
on the bearings. 



4^0 



ELEMENTARY LESSONS ON [chap. xv. 



486. Best Types of Dynamos and Motors Used on 
Various Kinds of Circuits. — 

I. CONSTANT POTENTIAL. 
(Machines, lamps, etc., run in parallel.) 



CIRCUIT 


POTENTIAL 


DYNAMO 


MOTOR 


Incandescent 


2- wire system, 


Plain shunt 


Plain shunt 


lamps 


110 volts 


or 






3 -wire system, 


compound 






220 volts 




Stationary 


Stationary 


) 


Plain shunt 


shunt 


motors 


[ 500 volts 


or 


Railroad 


Electric railroad 


) 


compound 


series 



II. CONSTAJ^T CURRENT. 
(Machines, lamps, etc., run in series.) 



CIRCUIT 


CURRENT 


DYNAMO 


MOTOR 


Arc lamps or 

stationary 

motors 


6.8 or 9.5 or 18 
amperes 


Series with 
current 
regulator 


Series with 

speed 

regulator 



CHAP. XV.] ELECTRICITY AND MAGNETISM. 



461 



487. Table of American Brown and Sharp Gauge. 

For pure hard drawn copper wire, temperature 0° C. 



Gauge 


Diameter 


Circular 


Section in 


Pounds 


Feet per 


Ohms 


Number. 


in inches- 


inches. 


sq. inches. 


per foot. 


pound. 


per foot. 


0000 


0.4600 


0.2116 


0.1662 


0.6412 


1.560 


0.00004629 


000 


.4096 


.1678 


.1318 


.5085 


1.967 


.00005837 


00 


.3648 


.1331 


.1045 


.4033 


2.480 


.00007361 





.3249 


.1055 


.0829 


.3198 


3.127 


.00009282 


1 


0.2893 


0.08369 


0.06573 


0.2536 


3.943 


0.0001170 


2 


.2576 


.06637 


.05213 


.2011 


4.972 


.0001476 


3 


.2294 


.05263 


.04134 


.1595 


6.270 


.0001861 


4 


.2043 


.04174 


.03278 


.1265 


7.905 


.0002347 


5 


.1819 


.03310 


.02600 


.1003 


9.969 


.0002959 


6 


0.1620 


0.02625 


0.02062 


0.07955 


12.57 


0.0003731 


7 


.1443 


.02082 


.01635 


.06309 


-15.85 


.0004705 


8 


.1285 


.01651 


.01297 


.05003 


19.99 


.0005933 


9 


.1144 


.01309 


.01028 


.03968 


25.20 


.0007482 


10 


.1019 


.01038 


.00815 


.03146 


31.78 


.0009434 


11 


0.09074 


0.008234 


0.006467 


0.02495 


40.08 


0.001190 


12 


.08081 


.006530 


.005129 


.01979 


50.54 


.001500 


13 


.07196 


.005178 


.004067 


.01569 


63.72 


.001892 


14 


.06408 


.004107 


.003225 


.01244 


80.35 


.002385 


15 


.05707 


.003257 


.002558 


.00987 


101.32 


.003008 


16 


0.05082 


0.002583 


0.002028 


0.007827 


127.8 


0.003793 


17 


.04526 


.002048 


.001609 


.006207 


161.1 


.004783 


18 


.04030 


.001624 


.001276 


.004922 


203.2 


.006031 


19 


.03589 


.001288 


.001012 


.003904 


256.2 


.007604 


20 


.03196 


.001021 


.000802 


.003096 


323.1 


.009589 


21 


0.02846 


0.0008101 


0.0006363 


0.002455 


408.2 


0.01209 


22 


.02535 


.0006424 


.0005046 


.001947 


513.6 


.01525 


23 


.02257 


.0005095 


.0004001 


.001544 


647.7 


.01923 


24 


.02010 


.0004040 


.0003173 


.001224 


816.7 


.02424 


25 


.01790 


.0003204 


.0002517 


.000971 


1029.9 


.03057 


26 


0.01594 


0.0002541 


0.0001996 


0.0007700 


1298. 


0.03855 


27 


.01419 


.0002015 


.0001583 


.0006107 


1638. 


.04861 


28 


.01264 


.0001598 


.0001255 


.0004843 


2065. 


.06130 


29 


.01126 


.0001267 


.0000995 


.0003841 


2604. 


.07729 


30 


.01003 


.0001005 


.0000789 


.0003046 


3283. 


.09746 


31 


0.008928 


0.00007970 


0.00006260 


0.0002415 


4140. 


0.1229 


32 


.007950 


.00006321 


.00004964 


.0001915 


5221. 


.1550 


33 


.007080 


.00005013 


.00003937 


.0001519 


6583. 


.1954 


34 


.006304 


.00003975 


.00003122 


.0001205 


8301. 


.2464 


35 


.005614 


.00003152 


.00002476 


.0000955 


10468. 


.3107 



PROBLEMS AND EXERCISES. 463 



PROBLEMS AND EXERCISES. 

QUESTIONS ON CHAPTER I. 

1. From what is the word ^^ electricity^^ derived? 

2. Name some of the different methods of producing electri* 
fi cation. 

3. A*body is charged so feebly that its electrification will not 
perceptibly move the leaves of a gold-leaf electroscope. Can 
you suggest any means of ascertaining whether the charge of the 
body is positive or negative ? 

4. Describe an experiment to prove that moistened thread 
conducts electricity better than dry -thread. 

5. "Why do we regard the two electnc charges produced 
simultaneously by rubbing two bodies together as being ol 
opposite kinds ? 

6. Explain the action of the electrophorus. Can you suggest 
any means for accomplishing by a rotatory motion the operations 
of lifting up and down the cosrer of the instrument so as to obtain 
a continuous supply instead of an intermittent one, ^ 

7. Explain the Torsion Balance, and how it can be used to 
investigate the laws of the distribution of electricity. 

. 8. Two small balls are charged respectively with + 24 and 
- 8 units of electricity. With what force will they attract one 
another when placed at a distance of 4 cerHimetres from one 
another? Aits, 12 dynes. 

o. If these two balls are then made to touch for an instant 



.464 PROBLEMS AND EXERCISES. 

and then put back in their former positions, with what force 
will they act on each other ? 

Ans. They repel one another with a force of 4 dynes. 

10. Zinc filings are sifted through a sieve made of copper wire 
upon an insulated zinc plate joined by a wire to an electroscope. 
What will be observed ? 

1 1. Explain the principle of an air-condenser ; and state why 
it is that the two oppositely charged plates show less signs of 
electrification when placed near together than when dra^vn apart 
from one another, 

12. There are four Leyden jars A, B, Cj and D, of which A, 
B, and D, are of glass, C of guttapercha* A, B, and C, are 0/ 
the same size, D being just twice as tall and twice as wide 
as the others. A, C, and D, are of the same thickness of 
material, but B is made of glass only half as thick as A or D. 
Compare their capacities, , Ans, Take capacity of A as i ; 

that of B will be 2 ; 

that of C will be \ ; 

and that of D will be 4. 

13. How would you prove that there is no electrification 
within a closed conductor ? 

14. What prevents the charge of a body from escaping away 
at its surface ? 

1 5. Explain the action of Hamilton's mill. 

16. Two brass balls mounted on glass stems are placed half 
an inch apart.. One of them is gradually charged by a machine 
until a spark passes between the two balls. State exactly what 
happened in the other brass ball and in the intervening air up 
to the moment of the appearance of the spark. 

1 7. Define electric density. A charge of 248 units of elec- 
tricity was imparted^ to a sphere of 4 centims. radius. What is 
the density of the charge ? Ans, i '23 nearly. 



QUESTIONS ON CHAPTER II, 

I. A dozen steel sewing-needles are hung in a bunch by 
threads through their eyes. How will thev behave when hung 
over the pole of a strong magnet ? 



PROBLEMS AND EXERCISES. 465 



^ 2. Six magnetised sewing-needles are thrust vertically through 
six little floats of cork, and are placed in a basin of water with 
their N. -pointing poles upwards. How will they affect one 
another, and what will be the effect of holding over them the 
S. -pointing pole of a magnet ? 

3. What distinction do you draw between magnets an^. 
magnetic matter ? 

4. On board an iron ship which is la)dng a submarine tele- 
graph cable there is a galvanometer used for testing the continuity 
of the cable. It is necessary to screen the magnetised needle of 
the galvanometer from being affected by the magnetism of the 
ship. How can this be done ? 

5. How would you prove two magnets to be of equal 
strength ? 

6. The force which a magnet-pole exerts upon another 
magnet-pole decreases as you increase the distance between 
them. What is the exact law of the magnetic force, and how 
is it proved experimentally ? 

7. What force does a magnet-pole, the strength of which .is 
9 units, exert upon a pole whose strength is 16 units placed 
6 centimetres away ? - Ans. 4 dynes, 

8. A pole of strength 40 units acts with a force of 32 dynes 
upon another pole 5 centimetres awav. What is the strength 
of that pole ? Ans. 20 units. 

9. It is desired to compare the magnetic force at a point 10 
centimetres from the pole of a magnet with the magnetic force 
at 5 centimetres' distance. Describe four ways of doing this. 

10. Explain the phenomenon of Consequent Poles. 

li. In what direction do the lines of magnetic induction (or 
** lines of force") run in a plane in v/hich there is a single 
magnetic pole ? How would you arrange an experiment by which 
to test your answer ? 

12. What is a Magnetic Shell t What is the law of the 
potential due to a magnetic shell ? 

13. A steel bar magnet suspended horizontally, and set to 
oscillate at Bristol, made no complete oscillations in five 



466 PROBLEMS AND EXERCISES. 

minutes ; the same needle when set oscillating horizontally at 
St. Helena executed 112 complete oscillations in four minutes. 
Compare the horizontal component of the force of the earth's 
magnetism at Bristol with that at St. Helena. 

Ans. H at Bristol : H at St. Helena :: 484 : 784, 

14. Supposing the dip at Bristol to be 70'' and that at St. 
Helena to be 30°, calculate from the data of the preceding 
question the total force of the earth's magnetism at St. Helena, 
that at Bristol being taken as "48 unit. Ans. '307. 

[N.B. — The student should see Footnote i, on p. 216.I 

15. A small magnetic needle was placed magnetically north 
of the middle point of a strong bar-magnet which lay (magneti- 
cally) east and west. When the magnet was 3 feet away from 
the needle the deflexion of the latter was 2** ; when moved up 
to a distance of 2 feet the deflexion was 6°^ 30' ; and when only 
X foot apart the deflexion was 43**. Deduce the law of the total 
action of one magnet on another. 

16. Describe how the daily irregularities of the earth's mag- 
netism are registered at different statio>xr, for comparison. 



QUESTIONS ON CHAPTER III. 

1. Show that the total of the diff'erences of potential by con- 
tact in three simple voltaic cells joined in series is three times as 
great as the difference of potential in one cell, the materials 
being the same in each. 

2. How can local action and polarisation be prevented in a 
voltaic cell ? 

3. Supposing the length of spark to be proportional to the 
difference of potential, calculate from the data of Arts. 291 and 
178 how many Daniell's cells would be required to yield a 
sufficient difference of potential to produce a spark one mile long 
through air. Ans. 1692 million cells. 

4. On what does the internal resistance of a battery depend ? 
Is there any way of dinainishing it ? 

5. Twenty -four similar cells are grouped together in four 
rows, of six cells each ; compare the electromotive-force and the 



PROBLEMS AND EXERCISES. 467 

resistance of the battery thus grouped, with the electromotive- 
force and the resistance of a single cell. 

/Ins. The E.M.F. of the battery is six times that of 

one cell. The total internal resistance is one and 

a half times that of one cell. 

6. A piece of silk-covered copper wire is coiled round the 
equator of a model terrestrial globe. Apply Ampere's rule to 
determine in which direction a current must be sent through the 
coil in order that the model globe may represent the condition 
of the earth magnetically. 

Ans. The current must flow across the Atlantic from 

Europe to America, and across the Pacific from 

America toward India ; or, in other words, must 
flow always from east toward west.- 

7. A current of -24 amperes flows through a circular coil of 
seventy-two turns, the (average) diameter of the coils being 20 
centimetres. What is the strength of the magnetic field which 
the current produces at the centre of the coil ? 

Ans, I 'oS. 

8. Suppose a current passing through the above coil produced 
a deflection of 35° upon a small magnetic needle placed at its 
centre (the plane of the coils being in the magnetic meridian), 
at a place where the horizontal component of the earth's 
magnetic force is -23 units. Calculate the strength of the 
current in amperes. (Art. 200.) Ans, 0'035, 

9. The current generated by a dynamo-electric machine was 
passed through a large ring of stout copper wire, at the centre 
of which hung a small magnetic needle to serve as a tangent 
galvanometer. When the steam engine drove the armature of 
the generator at 450 revolutions per minute the deflection of the 
needle was 60**. When the speed of the engine was increased 
so as to produce 900 revolutions per minute the deflection was 
74". Compare the strength of the currents in the two cases. 

Ans, The current was twice as great as before, for tan 
74" is almost exactly double of tan 60°. 

10. The current from two Grove's cells was passed through 
a sine - galvanometer to measure its strength. When the con- 
ducting wires were of stout copper wire the coils had to be 
turned through 70° before they stood parallel to the needle. 
But when long thin wires were used as conductors the coils 

2 F 



468 PROBLEMS AND EXERCISES. 



only required to be turned through 9**. Compare the strength 
of the current in the first case with that in the second case 
when flowing through the thin wires which offered considerable 
resistance. Ans. Currents are as i to ^, or as 6 to i. 

11. A plate of zinc and a plate of copper are respective!}' 
united by copper wires to the two screws of a galvanometer. 
They were then dipped side by side into a glass containing 
dilute sulphuric acid. The galvanometer needle at first showed 
a deflection of 28**, but five minutes later the deflection had 
fallen to ii^ How do you account for this failing off? 

12. Classify liquids according to thei^- power of conducting 
electricity. 

13. Name the substances produced at the anode and kathode 
respectively during the electrolysis of the following substances : — 
WatcTy dilute sulphuric acid^ sulphate of copper (dissolved in 
water), hydrochloric d5«^ (strong), iodide jof potassium (dissolved 
in water), chloride of tin (fused). 

14. A current is sent through three electrolytic cells, the first 
containing acidulated water, the second sulphate of copper, the 
third contains a solution of silver in cyanide of potassium. How 
much copper will have been deposited in the second cell while 
2*268 grammes of silver have been deposited in the third cell? 
And what volume of mixed gases will have been given off at the 
same time in the first cell ? 

Ans, •6614 grammes of copper and 352 •» cubic centi- 
metres of mixed gas^. 

15. A current passes by platinum electrodes through three 
cells, the first containing a solution of blue vitriol (cupric 
sulphate), the second containing a solution of green vitriol 
(ferrous sulphate), the third containing a solution of ferric 
chloride. State the amounts of the different substances evolved 
at each electrode by the passage of 1000 coulombs of electricity 

Ans First Cell | Anode -0828 gramme of oxygen gas.- 
Ans. i^t7st L.eu, I Kathode -3261 gramme of copper. 

Second Cell, ^"^t^ .''^ST'^'^^ ""^ T^^""' 
' I Kathode •2898 gramme of iron. 

T7l' d C II \ A^^^® '3^75 gramme of chlorine. 
'I Kathode '1449 gramme of iron. 

16. A tangent galvanometer, whose ** constant" in absolute 
units was 0*080, was joined in circuit with a batteiy and an 



PROBLEMS AND EXERCISES. 469 



electrolytic cell containing a solution of silver. The current 
was kept on for one hour ; the deflection observed at the begin- 
ning was 36°, but it fell steadily during the hour to 34°. Sup- 
posing the horizontal component of the earth's magnetic force 
to be '23, calculate the amount of silver deposited in the cell 
during the hour, the absolute electro -chemical 'equivalent of 
silver being p*oil34. A71S, '526 gramme. 

17. A piece of zinc, at the lower end of which a piece of 
copper wire is fixed, is suspended, in a glass jar containing a 
solution of acetate of lead. After a few hours *a deposit of 
lead in a curious tree -like form ("Arbor Saturni '^) grows 
downwards from the copper wire. Explain this. 

18. Explain the conditions under which electpcily excites 
muscular contraction. How can the converse phenomenon of 
currents of electricity produced by muscular^ contraction be 
shown ? 



QUESTIONS ON CHAPTER IV. 

I« Define the untt of electricity as derived in absolute terms 
from the fundamental units of le^tgth^ mass^ and time, 

2. At what distance must a small sphere charged with 28 
units of electricity be placed from a second sphere charged \^ith 
56 units in order to repel the latter with a force of 32 dynes? 

Ans. 7 centimetres. 

3. Suppose the distance from the earth to the moon to be (in 
round numbers) 383 x 10® centimetres ; and that the radius 0/ 
the earth is 63 x 10^ centimetres, and that of the moon 15 x 
10^' centimetres ; and that both moon and earth .are chained 
until the surface density on each of them is of the average value 
of 10 units per square centimetre. Calculate the "electrostatic 
repulsion between the moon and the earth. 

4. A small sphere is electrified with 24 units of -f electricity. 
Calculate the force with which it repels a unit of + electricity at 
distances of I, 2, 3, 4, 5, 6, 8, and 10 centimetres respectively. 
Then plot out the ^^ curve of force ^^ to scale; measuring the 
respective distances along a line from left to right as so many 
centimetres from a fixed point as origin ; then setting ont c. 



470 PROBLEMS AND EXERCISEb. 

vertical ordinates the amounts you have calculated for the 
corresponding forces : lastly, connecting by a curved line the 
system of points thus found. 

5 Define electrostatic (or electric) ^^ potential ;^^ and calculate 
(by the rule given in italics in Art. 238) the potential at a point 
A, which is at one corner of a square of 8 centimetres' side, 
when at the other three comers B, C, D, taken in order, 
charges of +16, +34, and +24 units are respectively placed. 

Ans. 8, very nearly exactly* 

6. A small sphere is electrified with 24 units of + electricity. 
Calculate the /^/^^/^/ due to this charge at points i, 2, 3, 4, 5, 
6, 8, and 10 centimetres' distance respectively. Then plot out 
the ^^ curve of potentiaV^ to scale, as described in Question 4. 

7. What are equipotential surfaces ? Why is the surface oi 
^ insulated conductor an equipotential surface ? Is it always 
so? 

8. A sphere whose radius is 14 centimetres is charged until 
the surface density has a value of lO, What quantity of 
electricity is required for this ? Ans. 24, 640 units (nearly). 

9. In the above question what will be the potential at the 
surface of the sphere? (See last sentence of Art. 246.) 

Ans,^ 1760 (very nearly). 

10. In the case of question 8, what will be the electric force at 
a point outside the sphere and indefinitely near to its surface ? 
(Art. 251.) Ans. 1257 (very nearly). 

11. Suppose a sphere whose radius is 10 centimetres to be 
charged with 6284 units of electricity, and that it is then caused 
to share its charge with a non-electrified sphere whose radius is 
15 centimetres, what will the respective charges and surface- 
densities on the two spheres be when separated ? 

Ans. Small sphere, ^ = 2513*6, 5 = 2: 
Large sphere, q = 3770'4, ? = I-33- 

12. A charge of + 8 units is collected at a point 20 centi- 
metres distant from the centre of a metallic sphere whose radius 
is 10 centimetres. It induces a negative electrification at the 
nearest side of the sphere. Find a point inside the spliere such 
that if 4 n^ative units were placed there they would exercise 



PROBLEMS AND EXERCISES. 47t 

a potential on all external points exactly equal to that of the 
actual negative electrification. (See Art. 250.) 

Ans. The point must be on the line between the outside 
positive charge and the centre of the sphere and at 
5 centims. from the surface. 

13. Two large parallel metal plates are charged both 
positiyeiy but unequally, the density at the surface of A being 
! + 6, that at the surface of B being + 3. They are placed 2 
centimetres apart. • Find the force with which a + unit of 
electricity is urged from A towards B. Find also the work 
done by a + unit of electricity in passing from A to B. 

Ans. Electric force from A towards B = 1 8 '85 dynes; work 
done by unit in passing from A to B = 37*5 ergs. 

^ 14. What is meant by the dimensions of a physical quantity ? 
Deduce from the Law of Inverse Squares the dimensions of 
electricity ; and show by this means that electricity is not a 
quantity of the same physical dimensions as either matter^ energy^ 
ox force. 

15. Explain the construction and principles of action of the 
quadrant electrometer. How could this instrument be made 
self-recording ? 

16. One of the two coatings of a condenser is put to earth, 
to the other coating a charge of $400 units is imparted. It is 
found that the difference of potential thereby produced between 
the coatings is 15 (electrostatic) units. What was the capacity 
©f the condenser ? Ans, 360. 

17. What is the meaning oi specific inductive capacity \ Why 
does hot glass appear to have a higher specific inductive capacity 
than cold glass ? 

18. Compare the phenomenon of the residual charge in a 
Ley den jar with the phenomenon of polarisation in an electro- 
lytic cell. 

19. A condenser was made of two fiat square metal plates,; 
the side of each of them being 35 centimetres. A sheet of 
indiarubber '4 centim. thick was placed between them as a 
dielectric. The specific inductive capacity of indiarubbei 
l)eing taken as 2*25, calculate the capacity of the condenser. 

Ans. 548*8 electrostatic units. 



472 PROBLEMS AND EXERCISES. 



20. Calculate (in electrostatic units) the capacity of a mile ol 
telegraph cable the core being a copper wire of 'iS centim. 
diameter, surrounded by a sheathing of guttapercha -9 1 centim. 
thick. [k for guttapercha = 2-46; one mile =160,933 
centims.] ^;/j. 82 164 units. 

21. A Leyden jar is made to share iis charge with two other 
jars, each of which is equal to it in capacity. Compare the 
energy of the charge in one jar with the energy of the original 
charge. -^^^•^* ^^® ninth as great. 

22. A series of Leyden jars of equal capacity are charged 
'*m cascade." Compare the total e^/erg-y of the charge of the 
individual jars thus charged, with that of a single jar charged 
from the same source. 

23. Classify the various modes of discharge, and state the 
conditions under which they occur. 

24. Suppose a conaenser, whose capacity is 10,000 charged 
lo potential 14, to be partially discharged so that the potential 
fell to 5. Calculate the amount of heat produced by the 
discharge, on the supposition that all the energy of the spark 
is converted into heat.* Aus. -020357 of a unit of heat. 

25. Jtlow do changes of pressure affect the passage of electric 
sparks through air ? 

26. Why are telegraphic signals through a submerged cable 
retarded in transmission, arid how can this retardation be 
obviated ? 

27. How is the difference of potential between the earth and 
the air above il measured? and what light do sucli measure- 
ments throw on the periodic variations in the electrical state oj 
the atmosphere ? 

28. What explanation can be given of the phenomena of a 
thunderstorm ? 

29. What are the essential features which a lightnmg-con- 
ductor mi.st possess before it can be pronounced satisfactory ? 
And what are the reasons for insisting on these points ? 

30. How can the duration of an electric spark be measured ? 



PROBLEIMS AND EXERCISES. 473 



QUESTIONS ON CHAPTER V. 

1. Define jjiagnetic potettiial^ and find the (magnetic) potential 
due to a bar magnet lo centimetres long, and of strength So, 
at a point lying m a line with the magnet poles and 6 centi- 
metres distant from its N. -seeking end. Aits. Z^^^ 

2. A N. -seeking pole and a S. -seeking pole, whose strengths 
are respectively +120 and — 60, are in a plane at a distance 
of 6 centimetres apart. Find the point between them where 
the potential is = o ; and through this point draw the curve of 
zero potential in the plane. 

3. Define "intensity of the magnetic field." A magnet 
whose strength is 270 is placed in a uniform magnetic field 

whose intensity is '166. What are the forces which act upon 
its poles ? Alts, +45 dynes and — 45 dynes. 

4. Define ''intensity of magnetisation." A rectangular bar- 
magnet, whose length was 9 centimetres, was magnetised until 
the strength of its poles was 164. It was 2 centimetres broad 
and '5 centimetre thick. Supposing it to be uniformly magnet- 
ised throughout its length, what is the intensity of the magnet- 
isation? Ans. 164. 

5. Poisson suggested a two -fluid theory of magnetism, the 
chief point of the hypothesis being that in the molecules of iron 
and other magnetic substances there were equal quantities of 
two opposite kinds of magnetic fluid \ and that in the act of 
magnetisation the two fluids were separated. What facts does 
this theory explain ? What facts does it fail to explain ? 

6. A current whose strength in ** absolute " electromagnetic 
units was equal to 0*05 traversed a wire ring of 2 centimetres 
radius. What was the strength of field at the centre of the 
ring ? What was the potential at a point P opposite the 
middle of the ring and 4 centimetres distant from the circum- 
ference of the ring. Ans, y=:«i57i;V = ± 0'042i, 

7. What limits are there to the power of an electromagnet ? 

8. What is the advantage of the iron core in an electro- 
magnet? 

9. Assuming the effective coefficient of magnetisation of iron 



474 PROBLEMS AND EXERCISES. 

to be 20, calculate the strength of the pole of an electromagnet 
whose coils consist of 50 turns of wire of an average radius of 
I centimetre, when a current of *2 amperes passes through the 
coils, the core consisting of a bar 5 centimetres long and of i 
square centimetre of area in its cross section [see An. 328]. 

Ans. 528 units. 

10. Enunciate Maxwell's rule concerning magnetic shells, 
and from it deduce the laws of parallel and oblique currents 
discovered by Ampere. 

11. A circular copper dish is joined to the zinc pole of a 
small battery. Acidulated water is then poured into the dish, 
and a wire from the carbon pole of the battery dips into the 
liquid at the middle, A few scraps of cork are thrown in tc 
render any movement of the liquid visible. What will occur 
when the N. -seeking pole of a strong bar-magnet is held above 
the dish ? 

12. Roget hung up a spiral of copper wire so that the lower 
end /usf dipped into a cup of mercuiy. When a strong current 
was sent through the spiral it started a continuous dance, the 
lower end producing bright sparks as it dipped in and out of 
the mercury. Explain this experiment. 

13. It is believed, though it has not yet been proved, thai 
ozone is more strongly magnetic than oxygen. How could this 
be put to proof? 



QUESTIONS ON CHAPTER VI. 

1 . The resistance of telegraph wire being taken as 1 3 oAms 
per mile, and the E. M. F. of a Leclanche cell as 1'5 vo/^y 
calculate how many cells are needed to send a current of 12 
milli-amp'^res through a line 1 20 miles long ; assuming that the 
instruments in circuit offer as much resistance as 20 miles of 
wire would do, and that the return-current through earth meets 
with no appreciable resistance. Ans. 1 5 cells. 

2. 50 Grove's cells (E. M. F. of a Grove = 1 8 volt) are 
united ip series, and the circuit is completed by a wire whose 
resistance is 1 5 ohvis. Supposing the internal resistance of each 
cell to be 0*3 ohm^ calculate the strength of the current. 

Ans. 3 amp^rss. 



PROBLEMS AND EXERCISES. . 475 

3. The current running through an incandescent filament of 
carbon in a lamp was found to be exactly i amplre. The 
difference of potential between the two terminals of the lamp 
while the current was flowing v/as found to be 30 volts. What 
was the resistance of the filament ? 

4. Define specific resistance. Taking the specific .resistance 
of copper as' 1642, calculate the resistance of a kilometre of 
copper wire whose diameter is i millimetre. Ans. 20*9 ohms. 

5. On measuring the resistance of a piece of No. 30 B. W. G. 
(covered) copper w^ire, i8*l2 yards long, I found it to have a 
resistance of 3 '02 ohms. Another coil of the same wire had a resist- 
ance of 22*65 chftts ; what length of wire was there in the coil ? 

Ans. 135*9 yards. 

6. Calculate the resistance ot a copper conductor one square 
centimetre in area of cross- section, .and long enough to reach 
from Niagara to New York, reckoning this distance as 480 
kilometres. Ans, 78*8 ohms, 

7. You have given an unlimited number of Telegraph Daniell's 
cells (Fig. 77), their E. M, F, being I'l voli each, and their 
average internal resistance being 2 '2 ohms each. What will be 
the strength of the current when five such cells, in series, are 
connected through a wire' whose resistance is 44 ohms ? 

Ans, O'l ampere, 

8. Show in the preceding case that with an infinite number 
of cells in series^ the current could not possibly exceed 0*5 
%mp^re. 

9. The specific resistance of guttapercha being 3*5 x io23, 
calculate the number of coulombs of electricity that would leak 
in one century through a sheet of guttapercha one centimetre 
thick and one metre square, whose faces were covered with 
tinfoil and joined respectively to the poles of a battery of 100 
Daniell's cells. Ans. 97 coulomb, 

10. Six Daniell's cells, for each of v/hich E = 1*05 volts^ r= 
0*5 ohm^ are joined in series. Three wires, X,Y, and Z, v/hose 
resistances are severally 3, 30, and 300 ohms, can be inserted 
between the poles of the battery. Determine the current (in 
amplres) which fiov/s when each wire is inserted separately ; also 
determine that which flows when they are all inserted at once 
in parallel arc 



476 PROBLEMS AND EXERCISES. 



Ans, Through X i«05 amperes ^^i ^^z. 

Through Y 0'I909 „ „ 

Through Z 0*0207 ,, „ 

Through all three I'I05 ,, „ 

1 1. Calculate the number of cells required to produce a 
current of 50 mini-amperes ^ through a line 114 miles long, whose 
resistance is 12 J ohms per mile, the available cells of the battery 
Having each an internal resistance of 1*5 ohm^ and an E.M.F. of 
I '5 volt. Ans. 50 cells. 

12. You have 20 large Leclanche cells (E.M.F. = l'5 volty 
/'=o*5 ohm each) in a circuit in which the external resistance is 
10 ohms. Find the strength of current which flows {a) when 
the cells are joined in simpJe series ; {b) all the zincs are united, 
and all the carbons united, in parallel arc ; (c) when the cells are 
arranged two abreast (Le. in two files of ten cells each); (d) 
when the cells are arranged four abreast. 

Ans, (a) 1*5 ampere, 
{b) 0-1496 „ 
{c) 1-2 
(^)0702 „ 

13. With the same battery how would yon arrange the ceiJa 
in order to telegraph through a line 100 miles long, reckoning 
the line resistance as 12 J ohms per mile? 

14. I have 48 cells, each of i'2 volt E.M.F., and each of 
2 ohms internal resistance. What is the best way of grouping 
them together when it is desired to send the strongest possible 
current through a circuit whose resistance is 12 ohms? 

Ans. Group them three abreast. 

15. Show that, if we have a battery of n given cells each of 
resistance r in a circuit where the external resistance is R, the 
strength of the current will be a maximum when the cells are 
coupled up in a certain number of rows equal numerically to 

Vl^r -^ R. 

16. Two wires, whose separate resistances are 28 and 24, are 
placed in parallel arc in a circuit so that the current divides, 
part passing through one, part through the other. What resist- 
ance do they ofifer thus to the current ? Ans. 12*92 ohms. 

17. Using a large bichromate cell of practically no internal 
resistance, a deflection of 9* was obtained upon a tangent 



PROBLEMS AND EXERCISES. 477 

galvanometer (also of small resistance) through a wire whose 
resistance was known to be 435 ohms. The same cell gave a 
deflection of 5® upon the same galvanometer when a wire of 
unknown resistance was substituted in the circuit. What was 
the unknown resistance ? Ans. 790 ohms. 

18. In a Wheatstone's bridge in which resistances of 10 and 
100 ohms respectively were used as the fixed resistances, a wire 
whose resistance was to be determined was placed : its resist- 
ance was balanced when the adjustable coils v/ere arranged to 
throw 281 ohms into circuit. What was its resistance ? 

Ans, 28*1 ohms, 

19. A battery of 5 Leclanche cells was connected in simple 
circuit with a galvanometer and a box of resistance coils. A 
deflection of 40° kaving been obtained by adjustment of the 
resistances, it was found that the introduction of 150 additional 
ohms of resistance brought doWn the deflection to 29^ A battery 
of ten DanielFs cells was then substituted in the circuit and 
adjusted until the deflexion was 40** as before. But this time it 
was found that 216 ohms had to be added before the ^deflection 
was brought down to 29®, Taking the E.M.F. of a single 
Darnell's cell as i '079 volt, calculate that of a single Leclanche' 
cf ' Ans, I '499 volt. 

20. How are standard resistance coils wound, and why? 
What materials are they made of, and why? 

21. Three very small Dariiell*s cells gave, with a sine galvan- 
ometer (itself of no appreciable resistance), a reading of 57®. On 
throwing 20 ohms into the circuk the galvanometer reading fell 
to 25^ Calculate the internal resistance of the cells. 

Ans, 6*6 ohms each. 

22. A knot of telegraph cable was plunged in a tub of water 
and then charged for a minute from a battery of 120 Daniell's 
cells. The cable was then discharged through a long -coil 
galvanometer with a needle of slow swing. The first swing 
was 40^ A condenser whose capacity was \ microfarad was 
then similarly charged and discharged ; but this time the first 
swing of the needle was only over I4^ ^^at was the cs^acity 
of the piece of cable ? Ans. 0'934 microfarad, 

23. Using an absolute electrometer, Sir W. Thomson foimd 
the difference of potential between the poles of a Daniell's cell 



478 TROBLEMS AND EXERCISES. 

to be '00374 electrostatic units (C.G.S. system). The ratio of 
the electrostatic to the electromagnetic rniit of potential is given 

in Art. 365, being = ^. The volt is defined as 10^ electromag- 
netic units. From these data calculate the E, M. F. of a 
DanielPs cell in volts. Ans, 1*115 '^^^^* 

24. The radius of the earth is approximately 63 x lo^ centi- 
metres. The ratio of the electrostatic to the electromagnetic 
unit of capacity is given in Art. 365. The definition of the 
farad is given in Art. 323. Calculate the capacity of the earth 
(regarded as a sphere) in microfarads. 

Ans, 700 microfarads (nearly). 

25. The electromotive-force of a Daniell's cell was determined 
by the following process : — Five newly-prepared cells were set 
up in series with a tangent galvanometer, whose constants were 
found by measurement. The resistances of the circuit were also 
measured, and found to be in total 1 6 '9 ohms. Knowing the 
resistance and the absolute strength of current the E.M.F. could 
be calculated. The deflection obtained was 45°, the number of 
turns of wire in the coil 10, the average radius of the coils Ji 
centimetres, and the value of the horizontal component of the. 
earth's magnetism at the place was 0'i8 C.G.S. units. Deduce 
the E.M.F. of a Daniell's cell. 

Ans. I '0647 X 10^ C.G.S. units, or 1*0647 ^^^<^« 



QUESTIONS ON CHAPTER VII. 

1. I have seen a small chain in which the altemate links 
were of platinum and silver wires. When an electric current 
wus sent through the chain the platinum links grew red hot 
while the silver links remained cold. Why was this ? 

2. Calculate by Joule's law the number of heat units developed 
in a wire whose resistance is 4 ohms when a steady current of 
•14 amphre is passed through it for 10 minutes. 

Ans. *i I '2 units of heat. 

3. What sort of cells ought to be the best for providing 
currents to fire torpedo shots ? 

4. Explain why a regulator like that of Duboscq is employed 
in obtaining a steady voltaic arc. 



PROBLEMS AND EXERCISES. 479 



5. I once tried to obtain an electric light by using a battery 
of 3000 telegraph Daniell's cells in series, but without success. 
Why did this enormous battery power fail for this purpose? 
Could it have been made to give a light by any different arrange- 
ment of the cells ? 

6. A battery of 2 Grove's cells, a galvanometer, and a little 
electromagnetic engine, were connected in circuit. At first the 
engine was loaded, so that it could only run slowly ; but when 
the load was lightened it spun round at a tremendous speed. 
But the faster the little engine worked the feebler was the 
current indicated by the galvanometer. Explain this. 

7. A purrent of 9 amperes worked an electric arc light, and on 
measuring the difference of potential between the two carbons 
by an electrometer it was found to be 140 volts. What was 
the amount of horse-power absorbed in this lamp ? 

Ans. 1-69 H.-P. 

8. You have a lathe in your workshop which requires power 
to turn it. There is a stream of water tumbling down the hill- 
side, two miles off, with power enough to turn twenty lathes. 
How can you bring this power to the place where you want to 
use it ? 

9. What is the use of the electro-djoiamometer ? Assum- 
ing that the moment of the force acting on the movable coil of 
the.electro-d3niamometer is proportional to the- product of the 
strengths of the currents in the two coils, show that the work 
performed by a current is really measured by the electro- 
dynamometer of Marcel Deprez, in which one set of coils has a 
very small resistance and the other a very high resistance (con- 
sisting of many turns of fine wire), the latter being arranged as 
a shunt to the lamp, motor, or other instrument, in which the 
work to be measured is being done, the former having the 
whole current passed (hrough it. 



QUESTIONS ON CHAPTER VHL 

I. A strong battery - current is sent, for a few moments, 
through a bar made of a piece of antimony soldered to a piece 
of bismuth. The battery is then disconnected from the wires 
and they are joined to a galvanometer which shows a deflection. 
Explain this phenomenon. 



480 PROBLEMS AND EXERCISES. 



2. A long strip oi zinc is connected to a galvanometer by 
iron wires. One junction is kept in ice, the other is plunged 
into water of a temperature of So'^C. Calculate, from the table 
given in Art. 381, the electromotive-force which is producing 
the current. /ins, 690 microvolts. 

3. When heat is evolved at a junction of two metals by the 
passage of a current, how would you distinguish between the 
heat due to resistance and the heat due to the Peltier effect ? 

4. Sir W. Thomson discovered that when a current flows 
through iron it absorbs heat when it flows from a hot point 
to a cold point ; but that when a current is flowing through 
copper it absorbs heat when it flows from a cold point to a hot 
point From these two facts, and from the general law that 
energy tends to run down to a minimum, deduce which way a 
current will flow round a circuit made of two half-rings of iron 
and copper, one junction of which is heated in hot water and the 
other cooled in ice. 



QUESTIONS ON CHAPTER IX. 

1. Give the reasons which exist for thinking that light is dH 
electromagnetic phenomenon.^ 

2. How is the action of magnetic forces upon the direction 
of the vibrations of light shown ? and what is the difference 
between magnetic and diama^etic media in respect of their 
magneto-optic properties ? 

3. It was discovered by Willoughby Smith that the resistance 
of selenium is less when exposed to light than in the dark. 
Describe the apparatus you would employ to investigate this 
phenomenon. How would you proceed to experiment if you 
wished to ascertain whether the amount of electric effect was 
proportional to the amount of illumination ? 



QUESTIONS ON CHAPTER X. 

li The ends of a coil of fine insulated wire are connected 
with terminals of a long-coil galvanometer. A steel bar- magnet 



PROBLEMS AND EXERCISES. 481 

is placed slowly into the hollow of the coil, and then witndraw& 
suddenly. What actions will be observed on the needle of the 
galvanometer ? 

2. Round the outside of a deep cylindrical jar are coiled two 
separate pieces of fine silk -covered wire, each consisting of many 
turns. The ends of one coil are fastened to a battery, those of 
the other to a sensitive galvanometer. When an iron bar is 
poked into the jar a momentary current is observed in the 
galvanometer coils, and when it is drawn out another moment- 
ary current, but in an opposite direction, is observed. Explain 
these observations, 

3. A casement window has an iron frame. The aspect is 
north, the hinges being on the east side. What happens when 
the window is opened ? 

4. Explain the construction of the induction . coil. What 
are the particular uses of the condenser, the automatic break, 
and the iron wire core ? 

5. It is desired to' measure the strength of the field between 
the poles of an electromagnet which is excited by a current from 
a constant source. How could you apply Faraday's discovery 
of induction currents to this purpose ? 

6. What is meant by the term ** extra-currents?'' A small 
battery was joined in circuit with a coil of fine wire^ and a 
galvanometer, in whic^h the current *was found to produce a 
steady but small deflection. -An unmagnetised iron bar was 
now plunged into the hollow of the coil and then withdrawn. 
The galvanometer needle was observed to recede momentarily 
from its first position, then to return and to swing beyond it 
with a wider arc than before, and finally to settle down to its 
original deflection. Explain these actions. 

7. In what respect do dynamo -electric machines differ from 
magneto-electric machines ? Where does the inagnetism of the 
field -magnets come from in the former? Where does the 
dynamical energy of the currents come from in the latter ? 

8. The older magneto - electric machines produced only 
intermUtent currents, and 'these were usually alternating in 
direction. By what means do the more modem magneto-electric 
generators produce currents which- are continuous and direct? 



482 PROBLEMS AND EXERCISES. 

9. A compass needle, v/Iien set swinging, comes to rest 
sooner if a plate of copper is placed beneath it than if a plate of 
glass or wood lies beneath it. Explain this fact. 

10. Explain how it is that on making circuit the current 
rises only gradually to its full strength, especially if there Jire 
large electrovnagnets in the circuit. 

1 1 . Foucault set the heavy bron^i^e wheel of his gyroscope 
spinning between the poles of a powerful electromagnet, and 
found that the wheel grew hot, and stopped. What was the 
cause of this ? Where did the heat come from ? 

12. The strength of the field between the poles of a laige 
electromagnet was determined by the following meanFi : — A 
small circular coil, consisting of 40 turns of fine insulated wire> 
mounted on a handle, was connected to the terminals of a long- 
coil galvanometer having a heavy needle. On inverting this coil 
suddenly, at a place where the total intensity of the earth's mag- 
netic force v/as '48 unit, a deflection Ox* 6** was shown as the first 
swing ^of the galvanometer needle. The sensitiveness of the 
galvanometer was then reduced to y^^ by means of a shunt. The 
little coil was introduced between the poles of the electromagnet 
and suddenly inverted, when the first swing of the galvan- 
ometer needle reached 40^ What was the strength of the field 
between the pol^« ? Ans, 3157 units. 



QUESTIONS ON CHATTER XI. 

1. It is found that a single DanielPs cell will not electiolyse 
acidulated water, however big it may be made. It is found, on 
the other hand, that two.Daniell's cells, however small, v/ill 
sultice to produce continuous electrolysis of acidulated water. 
How do you account for this? 

2. Wlien a gramme of zinc combines with oxygen it gives 
out 1301 heat-units. When this zinc oxide is dissolved in 
sulphuric a-jid 369 more units are evolved. To separate an 
equivalent amount of copper sulphate into sulphuric acid and 
copper oxide requires 588 heat -units to be expended. To 
separate the copper from the oxygen in this oxide requires 293 
more heat-iinits. The absolute electro -chemical equivalent oi 
rinc is 0*0034x2 {see Ait, 212), and Joule's dynamical equivalent 



PROBLEMS AND EXERCISES. 4S3 

of heat is 42 x 10^. From these figures calculate the electro- 
motive foice of a Daniell's cell. 

Ans, I -I ^06 X 10^ C.G.S. units, or 
1. 1306. volL 

3. Explain the operation of charging a secondar)' battery. 
What are the chemical actions which go on during charging and 
during discharging ? 

4. IMost liquids which conduce electricity are decomposed 
(except the melted metals) in the act of conducting. How do 
you account for the fact observed by Faiaday that the amount 
of matter tran^feiied through the liquid and deposited on the 
electrodes is proportional to the amount of electricity trans- 
ferred through the Kquid ? 

5. Describe the process for multiplying by electricity copies 
of engravings on wood-blocks. 

6. How would you make anangemerrts for silvering spcoiiG 
of nickel-brcnze by electio-deposition ? 

QUESTIONS ON CHA.PTER XII. 

r. Sketch an arrangement by which a single line of wire can 
be used by an operator at either end to signal to the otlier ; the 
condition of working being that whenever you are njt sending 
a message yourself your instrument shall be /;/ chcuit with the 
line wire, arrd out ^circuit ^\ith the battery at your own end. 

2. What advantages has the Morse instrument over the 
needle iirstrnnieirts introduced into telegraphy by Cooke and 
Wheatstone ? 

3. Explain the use and construction of a relay. 

4. It is desirable in certain cases (diplex and quadniplex 
signalling) to arrange telegraphic instruments so that they will 
respond only to currents which come in one direction through 
the line. Il3w can this be done? 

5. A battery is set up at one station. A galvanometer neeale 
at a station eighty miles away is deflected through \ certain 
Lumber of degiees when the wire of its coil makes twelve turns 
round the needle ; wire of the same quality being used for 
both line and galvanometer. At 200 miles the same deflection 
I5 obtained when twenty - four t^irns are used in the gal van- 

2 G 



484 PROBLEMS AND EXERCISES. 

ometer-coil. Show by calculation (a) that the internal resist- 
ance of the battery is equal to that of 40 miles of the line-wire ; 
(d) that to produce an equal deflection at a station 360 miles 
distant the number of turns of wire in the galvanometer -coil 
must be 40. 

6. Suppose an Atlantic cable to. snap off short during the 
process of laying. How can the distance of the broken end 
from the shore end be ascertained ? 

7. Suppose the copper core of a submarine cable to part at 
some point in the middle without any damage being done to 
the outer sheath of guttapercha. How could the position of 
the fault be ascertained by tests made at the shore end ? 

8. Explain the construction and action of an electric bell. 

9. Describe and explain how electric currents are applied in 
the instruments by which very short intervals of time are 
measured. 

10. Explain the use of Graham Bell's telephone (i) to 
transmit vibrations ; (2) to reproduce vibrations. 

11. Describe a form of telephone in which the vibrations of 
sound are transmitted by means of the changes they produce in 
the resistance of a circuit in which there is a constant electro- 
motive-force, 

12. Two coils, A and B, of fine insulated wire, made exactly 
alike, and of the same number of windings in each, are placed 
upon a common axis, but at a distance of 10 inches apart. They 
are placed in circuit with one another and with the secondary wire 
of a small induction-coil of RuhmkoiiTs pattern, the connections 
being so arranged that the currents run round the two coils in 
opposite directions. A third coil of fine wire, C, has its two 
ends connected with a BelPs- telephone, to which the experi- 
menter listens while he places this third coil between the other 
two. He finds that when C is exactly midway between A and 
B no sound is audible in the telephone, though sounds are 
heard if C is nearer to either A or B. Explain the cause of this. 
He also finds that if a bit of iron wire is placed in A silence is 
not obtained in the telephone until .C is moved to a position 
nearer to B than the middle. VVhy Is this? Lastly, he finds 
that if a disc of brass, copper, or lead, is interposed between A 
and C, the position of silence for C is now nearer to A than the 
middle. How is this explamed ? 



INDEX. 



INDEX TO CHAPTERS I-XIII. 



N.B. — The Figures refer to the Numbered Paragraphs. 



Absolute Electrometer, 261 
Galvanometer, 200 
Measurements, 325a, 363, 364 
Units of Measurement, 255 

Accumulator, 47, 48, 266 

of currents (see Secondary 
Batteries) 

Action at a distance, 21, 56, ^72 

Air condenser,. 48, 267 

Air, resistance of, 291, 325b 

Aldini^ Giovanni, Experiments on 
Animals, 229 

Amalgam, electric, 41 

Amalgamating zinc plates, 162 

Amber, i 

Amoeba, the sensitiveness of, 230 

Am-meter, 200 {bis) 

AmperCy Andri^ Theory of Electro- 
dynamics, 331, 334 
''Ampere's Rule," 186 
Laws of Currents, 332 
suggests a Telegraph, 423 
Table for Experiments, 333 
Theory of Magnetism, 338 
Ampere, the, 323 

Angles, Ways oi Reckoning, 129 
Solid, 133^ 

Animal Electricity, 68, 231 

Anion, 210 

Annual variations of magnet, 143 

Anode, 207 

Arc, voltaic, 371 

AragOy Francois J cany 

classification of lightning, 304 
magnetisation by current, 326 
on magnetic action of a voltaic 

current, 191 
on magnetic rotations, 401 



Armature of magnet, loi 

of dynamo - electric machine, 
407, 409, 410 
Armstrongs Sir IVm,, his Hydro- 
electric Machine, 44 , 
Astatic magnetic needles, 190 

Galvanometer, 190 
Atmospheric Electricity, 64, 301, 306 
Attracted-disc Electrometers, 261 
Attraction and repulsion of elec- 
trified bodies, I, 3, 18, 20, 
66y 236 
and repulsion of currents, 331, 
and repulsionof magnets, 76, 80 
332 
Aurora, the, 144, 145, 309 
Ayrton (IV. £.) and Perry {John) 
on contact electricity, 72 
on dielectric capacity, 271 
value of "z/,** 365 
am-meter, 200 {bis) 
voltmeter, 360 {d) 
Azimuth Compass, 134, 136 



B. A, Unit (or ohm), 323, 363, 364 

Back Stroke, 26, 304 

Bain's Chemical Writing Telegraph, 

218 
Balance, IVheatsione's, 358 
Ballistic Galvanometer, 204 
Bancalarion. diamagnetism of flames, 

344 
Battery of Leyden Jars, 54 
Batteries, voltaic, 154, 167, 182 
,, list of, 178 
secondary, 415 " 
Beccaria, Father G-y on eiectric 
distillation, 223 



486 



INDEX. 



BeccariUt Father d on atmospheric 

electricity, 306 
BecquereL Antoine Cesar^ on atmo- 
spheric electricity, 307 
oi^diamagnetism, 339 
Becquerelf Edtnotid^ on photo- voltaic 

currents, 389 
Becq tiered Henri, on magneto-optic 

rotation, 387 
Bellf Alexander Graham^ his Tele- 
phone. 435 ^ 
The ' Phptophone, 38^ 
Bells, electric, 432 
Bennefs Doubler, 23 

Electroscope, 13, 25 
Bertsch's Electric Machine, 45 
Best grouping of cells, 351 
Bichromate Battery,, 165 
Bifilar Suspension, 118, 262, 336 
Biotf Jean Baptiste^ Exporiment with 
he^ii spheres, jo 
Law of magnetic distribution, 

^1^8 
en atmospheric electricity, 307 
Bismuth, diamagnetic properties of, 

87, 313 339 _ 
Blasting by electricity, 280, 370 
Blood, diamagnetism of, 339 
.Boracite, 67 

*' Bound" electricity, 24^^ 149 {foot- 
note) 
Boltzmann, on Dielectric capacity, 

270, 271, 390 
BoyUy Hpn» Robert , on electrical 

attraction, 2 
Branched circuif, 353 
Breaking a magnet, 106 
Breath-figures, 297 
Bridge, Wheatstone*^^ 358 
British Association Unit, 323, 364, 

Brugtnans discovers magnetic repul- 
sion , of bisniufh, 339 
Brush discharge, 290 
Brush* s dynamo-electric machine, 41 1 
Bunsen*s Battery, 172 



Cable, Atlantic, 274 (Jbotnote), 275, 
296, 429 
submarine, 429 

„ as condenser, 274, 

296, 430 
Cabot, iiebasimn^ on magnetic de- 

'clination, 136 
Cailletet on resistance of air, 291 
Calibration of Galvanometer. xo8 



Callan*s Battery, 172 
Callauds Battery, 176' 
CajttoHi John^ discovers £IectrosGi]tic 
Induction, 18 ^ 

on Electric Amalgam, 4* 
Candle, electric, 373 
Capacity, definition of, 246 

measurement of, 362 

of accumulator or condenser, 
50, 267, 277 

of conductor, 37, 47, 247, 277 

of Leyden Jar, 50, 267 

specific inductive, 21, 49, 268 
272 

unit of (electrostatic), 247 

unit of (practical), 276 
Capillary Electrometer, 225, 265 
Carnivorous Plants, sensitive tcTelec- 

tricity, 230 
Carrit F., Dielectric machine, 45 

on magnets of cast mctaJ, 97 
Cascade arrangement of Jars, 279 
Cautery by electricity, 369 
Cavallo Tiberius, his attempt to 
telegraph. 423 

his pith -ball electroscope, 3 

on a fireball, 304 

on atmospheric electricity, 302, 
306 
Cavendish, Hon, H,, on Specific 
Inductive capacity, 268, 269 

on nitric acid produced by 
sparks, 286 
Ceca, * Father, on atmospheric eft^ 

tricity, 306 
Cell, voltaic, 152 
Charge, electric, 7 

resides on surface, 27 

residual of Leyden Jar, 53^ 27a 
Chart, magnetic, 136, 169 
Chemical actions in the oattery, 159 

laws of 166, 211, 417 

of sjjark discharge, 286 

outside the battery, 205, 412 
Chemical test for weak currents, 218, 

286 
Chimes, electric, 43 
Chronograph, electric, 433 
Circuit, 152 

simple and compound, 181 
Clark's {Latimer) standard cell, 177 
Clausius, R,, theory of Electrolysis, 

418 • 

Cleavage, electrification by, 60 
Clocks, electric, 433 
Cobalt, magnetism of, 86 
Coefficient of Magnetic induction, 89 

313 
of muttial induction, 39a 



INDEX. 



487 



Coercive force, 89 

Colour of spark, 28J 

Columbus^ C risto/erOi on magnetic 

variation, 136 
Combustion a source of electrification, 

02 
Commutator, 375, 399, 407 ^ 
Compass (magnetic). Mariner's, 79, 

134 ' . . 

Compound curcuit, 181 
Condensation 48 
Condensers, 48, 267 

standard, 276 

use of, 275 
Condensing electrorcope, 71, 149 
Conduction, 27, 158 

by liquids, 205 

of gases, 158 
Conductivity, 158, 346, 348 
Conductors and Non-conductors, 8, 27 
Consequent Poles, 104, 109 
Contact Electricity, 71, 149 

Series of metals, 72 
Continuous electrophorus, 23, 45 
Convection of Electricity, 45, 337 
Convection-currents, properties of, 337 
Convection-induction machines, 45 
Convection-streams at points, 35 (a), 

43» 249 , . 
Cooling and heating of junction by 

current, 380 
Cost of power denved from electricity, 

378 
Coidomh^ Torsion Balance, 15, 119 
Law of Inverse Squares, 16, 

117, 119, 235, 245 
on distribution of charge, 35, 248 
Coulomb, the, 32 s 
Couple, magnetic, 123 
Cfookea^ ll^illiam, on shadows in 
electric discharge, 293 
on repuhion from negative 
electr'".ie, 300 
Crown of cups, 151 
Cruickahank' i Trough Batter>^ 160 
Crystals, electricity of, 66 

dielectric properties of, 270 
magnetism of, 343 
Cryotcilli nation, 61 
CumtniHg s phenomenon, 382 
Cuneui,' discovery of Ley den Jar, 52 
Current, effect? «lue 10, 153 
Current Electricity. 147 

strength of, 158, 1^9 

,, unit 01, 196 
Current-rev er»er (see Commutator) 
Current sneets, 340 
Curvature aifects surface-density, 35, 
249 



Curves, magnetic (see Magnetic 

Figures) 
CuthbertsorCs Electric machine, 38, 

289 
Cylinder Electrical machine, 39 



Daily variations of magnet, 14? 
/?a//3«n/'5 lightning-rod. 302 
DanleWs Battery, 170 
Davy 5 (Marie) Battery, 175 
Davy, Sir Humphrey, magnetisation 
biy current, 326 
discovers electric light, 371 
electrolyses caustit alkalies, 

417 w 

De Haldat. magnetic writing, iii 
De la Rive s Floating Battery, 194 
DelaRue, Chloride of Silver Battery, 
174, 291 

on electrotyping, 420 

on length of spark, 291 
Declination, Magnetic, 136 

variations of, 136, 141 
Decomposition of water, 206, 413 

of alkalies, 417 
Deflections, method of, 118, 123, 325a 
Dellmann^s electrometer, 260 
Density (surface) of charge, 35, 248 

magnetic, 127, 311 
Dewar, James, on currents generated 
by light Li the eye, 231* 

his capillary electrometer, 225 
Diagram, thermo-electric, 383 
Diamagnetic polarity, 342 
Diamagnetism, 87, 339 

of flames, 544 

of gases, 340 
Diaphragm currents, 224 
Dielectric capacity (see Specific In 
ductive Capacity) 

strain, 56, 272 

strength, 284 
Dielectrics, 8, 49, 270 
Diff"erential Galvanometer, 203 
Dimensions of Units (see Units) 
Dip, or Inclination, 137 

variation of, 141 
Diplex signalling, 428 
Dipping Needle, 137 
Discharge atfected by magnet,^94 

brush, 43 

by evaporation, 223 

by flame, 7, 291 

conductive, 282 

convective, 43, 283 

disruptive, 381 



INDEX. 



Discharge affected by points, 43, 390, 
302 

effects of» 43, 384, 386 

electrical, 7, sSo 

glow, 2po, 302 ijbotnote) 

umit of; 248 

iensitive state of, 294 

velocity of, 296 
31scliarger, Discharging-tongs, 51 

Universal, 54 
Disruption produces electrification, 60 
Dissectable Leyden Jar, 55 
Dissipation of Charge, 299 
Distillation, electric, 225 ^ 
Distribution of Electricity, 28, 35, 
248, 249 

of Current, 240 

of Magnetbm, 104, 122 
Divided Circuit, 353 

Touch, 93 
Dolbeaf^s Telephone, 436 
Doubler, 23, 45 
Double Touch, 94 
I>ry-Pile, 182, 264 
Duboscq^s Lamp, 372 
Vu Fa/s experiments, 4, 27 
Duplex Telegraphy, 275, 428 
I^uration of Spark, 296 
ID^uier on Electric Expansion, 273 
Dynamic Electricity (see Current 

Electricity) 
Dynamo-electric machine's, 408 
Dyne, the (unit of force), 255 



Earth, the, a magnet, 88 
currents, 2^5, 403 ^ 
electrostatic capacity of, 325b 
intensity of magnetisation, 313 
magnetic moment of,* 325b 
used as return wire, 423 

Earth's magnetism {s^^'^Terresirial 
Magnetism) 

Edison, Thomas A Iva^ ^QCtriclaxti'Pf 
374 ; steam-dynamo, 411 (5'" 
carbon telephone, 436 
meter for currents, 216 
quadruplex telegraphy, 428 

Edlund on galvanic expansion, 221 

Eel, electric (Gymnotus), 68 

Electrics; z 

Electric Air-Thermometer, 288 
Cage, 34 
Candle, 373 
Clocks, ^33 
Distillation, 333 
(Frictional) machines, 39 



Electric Egg, the, 29a 
Expansion, 273 
Force, 155 {/ootnoie\ 841 
Fuze, 286, 370 
Images, 2^0 
Kite, 302 
Lamps, 372 
Light, 371 
Mill or Fly, 43 
Oscillations, 295 
Osmose, 222 
Pistol, 386 
Shadows, 293 
Shock, 226 
Wind, 43 
Electricity, theories of, 6, 300 
Electro-capillary phenomena, 225 
Electro-chemic^ equivalents, 211, 21 s 
Electro-chemistry, 412 
Electrodes, 207 

unpolarisable, 231 
Eiectrodjmamics, 331 
Elcctrody^amometer, 336,378 {his,) 
Electrolysis, 208 

laws of, 211, 414, 417 
of copper sulphate, 209 
of water, 207, 413 
theory of, 414 
Electrolytes, 207, 417 
Electrolytic convection, 4s 3 
Electromagnets, 98, 326 

laws of, ^30 
Electromagnetic engines (motors), 375 
Electromagnetics, 3x0 
Electromagnetic theory of Light, 390 
Electromagnetism, 326 
Electrometallurgy, 419 
Electrometer, absolute, 261 
attracted-disc, 261 
capillary, 225, 265 
Dell9Hann*5f 260 
divided-ring, 71 
Peltier's, 260, 307 
portable, 261 
quadrant {Sir W, Thonisofii^x 

262 
repulsion, 260 
torsion, 15 
trap-door, 261 
Electromotive-force, 155 

measurement of, 360 
unit of, 322, 323 
Electromotors, 375 
Electro-Optics, 385 
Electrophorus, 22 

continuous, 23, 45 
Electroplating, 421 
Electroscopes, 11 

Bohnenbergef' s, 13* a64 



INDEX. 



4^9 



Electroscopes, Bennefs gold-leaf, 13, 

25 

Fechner^s, 264 

Gangain*s discharging, 259 

Gilberts straw-needle, 12 

HankeVsy 264 

Henley s quadrant, 14 

Pith-ball, 2, 3 

VoltcCs condensing, 71, 149 
Electrostatics, 7, 233 
Electrotyping, 420 
Energy of charge of Leyden Jar, 270 

of electric current, 378 
Equator,^ Magnetic, 78 
Equipotential surfaces, 242, 310 (f) 

magnetic, 310 
Equivalents, electro -chemical, 212 
Erg, the (unit of work), 255 
Evaporation produces electrification, 

63* 303- 
discharge by, 223 
Everett, James D,, on atmdipheric 
electricity, 307 
on exact reading of galvan- 
ometer, 202 (footnote) 
on intensity of magnetisation 
of earth, 313 
Expansion, electric, 273, 386 
Extra-ctirrent (self-induced), 404 



P 

Failure and exhaustion of batteries, 

160 
Fall of Potential along a wire, 263, 357 
Farad, the (unit of capacity), 276, 323 
Faraday^ Michael, molecular theory 
of electricity, 6 
chemical theory of cell, 166 
dark discharge, 290 
Diamagnetism, 33^, 340, 344 
, discovered inductive capacity, 
21, 269, 271 
Discovery of magneto •induc- 
. tion, 391 

Electro-magnetic rotation, 375 
experiment on dielectric polar- 
isation, 272 
gauze-bag experiment, 31 
hollow-cube experiment, 31 
ice-pail experimeni, 34 
laws of electrolysis, 211, 214 
Magnetic lines-Qf-foifce, io8, 402 
on Aragds rotations, 401 
on dissi{)ation of charge, 291 
on identity of different kinds of 

electricity, 217, 218, 286 
Yolrameter, 214 



Faraday, Michael, Magneto -optic 

discovery, 387 
predicted retaraation in cables, 

274 
/?Vr«r^j Secondary Battery, 415 

Favr^s experiments on Heat of Cur- 
rents, 368 
Fechner^s electroscope, 264 
Feddersen, IV., on electric oscilla- 
tions, 296 
Ferromagnetic substances, 339 
Field, magnetic, 105, 191, 312 
Figures, magnetic (see Magnetic 
figures) 
electric, 297 
Fire of St. Elmo, 302 (footnote) 
Flame, currents of, 291 

diamagnetism of, 344 
discharge by, 7, 291 
produces electrification, 62 
Fleming's Battery, 182 
Fontana on electric expansion, 273 
Force, electric, 155 (footnote), 241, 
251, 252 
magnetic, 83, 155 (footnote)^ 

328 
electromotive, 155 
Foucaulfs Regulator Lamp, 372 

Interruptor, 398 
Franklin, Benja7nin, discovered 
action of points, mentioned 
in, 35(c), 43, 302 
cascade arrangement of Leyden 

Jars, 279^ 
Electric Chimes, 43 
Electric Kite, 502 
Electric portraits, 288 
his charged pane of glass, 47 
invents Lightning Conductors, 

.305 
kills turkey by electric shock, 

2f6 

One-fluid theory of Electricity, 

• ^ 

on seat of charge, 55 
theory of the Aurora, 309 
" Free " electricity, 24, 149 (footnote) 
Friction produces electrification, i, ro 
Frog's legs, contractions of, 148, / 
Fromenfs Electromotor, 375 
Fuze, electric, 286, 370 



Gaivani, Aloysius\ observed mOVO* 
ments of frog's leg, 148 



49o; 



INDEX. 



Galvaniy AloystuSy on preparation of 
frog's limbs, 22p 
on Animal Electncitj", 231 
Galvanic Batteries (see Voltaic 
Batteries) 
Electricity (see Current E he- 
ir icity) 
Taste, 227 
Galvanism (see Current Electricity) 
Galvanometer, iq/ 
absolute, 200 
astatic, 19S, 23s 
ballistic, 204 
constant of, 200 
differential, 203 
r>ii B )i<' Reytnofid^Sf 231 
Heljuholtzs, 190 
reflecting {Sir Jr. Thomso7^s\ 

or mirror, 202 
sine, 201 
tangent, 199 
Galvanoplastic (see Electrotyping) 
Galvanoscope, 188 
Gas Battery, 416 
Gases, resi.uance of, 158 
Gassiot^ J, P , nn strics, 294, 300 
Gaugain^ Jean Mothie^ discharging 
electroscope, 259 
on Pyroelectricity, 66 
Tangent Galvanometer, 199 
GausSy E.f invented absolute measure- 
ment, 325a 
magnetic moment of earth, 

325b 
magnetic observations, 313 
Cay^ Lussac, on atmospheric elec- 
tricity, 307 
Geiss/er*s tubes, 291 
Genrez on electric distillation, 223 
Gibson and Barclay on dielectric 

capacity of paraftin, 270 
Gilbe7t, Dr, Williain^ discovers 
electrics, i, 
discovered magnetic reaction, 

discovers that the earth is a 

magnet, 88, 135 
heat destroys magnetism, 09 
his balanced - needle electro- 
scope, 12 
observation of moisture, 9 
observations on magnets, 78 
on de - electrifying power of 

flame, 291 
on magnetic figures, 108 
on magnetic substances, 85 
on magnetic permeability, 84 
on methods of magnetisation, 
96. 97 



Gilding by Electricity, 431 

Globular lightning, 304 

Glow Discharge, 290, 302 (^footnote) 

Glowing of wires, 369 

Gold-leaf Electroscope (see Electro- 

scope) 

Gordon y /. E, //., on magneto-optic 

rotatory power, 587 

on dielectric capacity. 270, 271 

on length of spark, 291 

Gramme's dynamo-electric machine, 

410 
Gravitation Battery, 176 
Gray^ Stephen^ discovers conduction, 
27 
on lightning, 302 
Grotthuss* theory, 160, 418 
Grove ^ Sir William ^,, his ,Gas 
Battery, 416 
Groves Battery, 171 
magnetic experiment, 113 
en electric property of Flame, 
291 
Guard-ring, Guard-plate, 248, 261 
Guerickey Otto von^ discovered elee 
trie repulsion, 3 
invents electric machine, 38 
observes electric sparks, 9 
Gunpowder fired by electricity, 286, 

288, 370 
Gymnotus (electric eel), 68, 2x8 



Halts phenomenon, 337 
Hanker s electroscope, 264 
Harris^ Sir W, Sftovit his unit 
Leydenjar, 259 
attracted • disc electrometer, 

261 
on length of spark, 291 
Heat, eflfect of, on magnets, 99, 100 
„ batteries, 183 

„ conductivity, 349 

Heating eflfects of currents, 171, 366, 
380 
due to magnetisation, 1x3, 401 
eHect of sparks, 288 

,, dielectric stress, 272 
local, at electrodes, 41' 
Helmkoltz, Hermann L, on 

eflfect of current on s% , 22R 
Electrolytic convection, 418 
Equations of Self-induction, 

405 
Galvanometer, 199 
Hcnry^ Joseph^ invented thu 
** sounder," 423 



INDEX. 



401 



Henry ^ Joseph^ on induced currents of 

higher orders, 406 
Hoitz^ W,, his electric machine. 46 
on electric shadows, 293 {^foot- 
note) 
on tubes having unilateral re- 
sistance, 300 
HopktnsoKy John^ on dielectric cap- 
acity of glass> 270 
on residual charge and its 
return, 53, 272 
Horizontal component of magnetism, 

Hughes t David Edward^ the Print-, 
ing Telegraph, 423 
the Microphone, 437 
Humboldt i Alexander von, on elefc- 
tric eels, 68 
discovers galvanic smell, 228 
produced electric contractions 
in fishes, 229 
Hunter, Dr,^ John, on effect of 

current on sight, 228 
Hydroelectric machine, 44 



Images, electric, 250 
Incandescent electric lights, 374 
Inclination (or Dip), 137 

variation of, 141 
Index Notation, 325b 
Induced charges of electricity, x8 

currents, 391 
Induction {electrostatic) of charges, 
x8 

{mag>utic\ lines of, 89 

{magnetic) of magnetism, 89, 

„ coemcient of, 342 

(magneto-electric) of currents. 

Induction-coil or Inductorium, 398 
Induciion-convsction machines, 45 
Ind ictjve-capacity, specific, 21, 49, 

;*oS 272 

In&ulat'irs, 8, 27 
inten:»uy of current, 179 

ai earth's magnetic force, 138, 
325a 

ol magnetic field, 312 

of magnetisation, 3x3 
Inverse Squares, Law of, 16, 117, 235, 

245 
Inversion, Thermo-electric, 382 
Ions, 210 

Isoclinic lines, X39 
Isogomc lines, 139 



Jacohi, Moritz Hermann, on local 
action, x62 
discovers galvanoplastic pro- 
cess, 420 
his boat propelled by electricity, 

theory of electromotors, 377 
Jahlochko^^ Paul^ his battery, 183 

electric candle, 373 
Jar, Leyden, 51 

^ capacity of, 50, 267, £77 
„ cascade arrangement cf, 

279 
„ cUscharge of, 51, 293 
„ discovery of, 52 
„ energy of charge of, cjS 
„ seat of charge of, 55 
„ spark of, 289, 296 
„ theory of, 267 
Unit, 259 
Jenkin, Fleeming, on cable as con- 
denser, 2;^4 
on retardation in cables, 296 
Joule^ James Prescott^ on effects of 
magnetisation. 1x3 
Law of Heat of Current, 367 
Mechanical equivalent of Heatj 

255, 414 
on atmospheric electricity, 306 
on lifting - power of electro- 
magnet, 32b 
/^^/if-efFect, the, 380, 367 



Rathodb, ao7 
Kation, 210 
Keeper, loi 

AVrr, Dr* John, Electro - optic dis- 
coveries, 273, 386 
Magneto-optic discoveries, ixa, 
388 . 
Kinnersley, Elijah^ Electric Ther- 
mometer, 288 
Kirihhoff, Gustav^ Laws of Branched 

Circuits, 353 
Kite, the electric, 302 
Kohlrausch, F,, on residual charge, 
272 
on electro-chemical equivalent, 
211 ijbotnpte) 



Lambllar magnetisation, 107 



492 



INDEX, 



Laminated magnets, 95 

Law of Inverse squares, x6, 1x7, 235, 

245 
Leakage, rate of, 299 
Leclanchi*s Battery,^ 173 
Le Baillif on diaroagnetism of 

antimony, 33^ 
Lemonnier discovers atmospheric 

electricity, 306 
Length of spark, 291 
Lenses Law, 396 

alcohol calorimeter, 367 
Leyden Jar (see Jar) 
Lichtenher^s figures, 297 
Lifting-power of magnets, 103 

of electromagnets, 328 
Light affects resistance, 389 
' Electric, 371 
Electromagnetic theory of, 365, 

390 

polarised, rotated by magnet, 
114, 387, 388 
Lightnmg, 9, 302, 304 

conductors, 32, 305 

duration of, 296, 304 
Lines-of-force, electric, 243 

due to currents, 191, 329, 334 

magnetic, 89, 108, 310, 312 
Lippmann^ G., Capillary Electro- 
meter, 225, 265 
Liquids as conductors, 205 

resistance of, 348 
** Local Action " in batteries, 161 
Lodestone, 76, 340 
** Long-coil instruments, 352 
Loss of Charge, 15, 259 
Lffuis XV, electrifies 700 monks, 226 
LullirHs experiment, 285 
Luminous effects of spark, 289, 400 

M 

Machine, Alternate-current, 411 

Electric, 38 

Compound- wound, 411 

convection-induction, 45 

cylinder, 39 

dynamo-electric, 408 

Holts^s, 46 , 

hydro-electrical, 44 

invention of, 38 

magneto-electric, 407 

plate, 44 

Winters, 40 
Magne-crystallic action, 343 
Magnet, breaking a, 106 
Magnets, natural and artificial, 76, 

77* 326 
Magnetic actions of current, 18^; 318, 
326, 329, 334 



Magnetic attraction and repulsion, 80, 

no 
cage, 84 
curves, 108, 191 
field, 105, 191, 312, 327^ 
figures, 108, 109, izo,i9z 

„ theory of, 126 
fluids, allegea, 91 
force, 83, 310 (e) 

„ measurement of, 118 
. 325a 
mduction, 89 

„ coefficient of, 342 
iron ore, 76 

lines-of-force, 89, zoS, Z09, zzo» 
^ 316 
lines-of-force of current, zgz, 

320, 329 
maps, 139 
meridian, Z36 
metals, 86, 339 
moment, Z23 {footnote^ 3Z3, 

325a 
needle, 79, Z34 

oxide of iron, 76, 172 [Jootno*^) 
paradox, a, Z28 
pole, unit, X25 
potential, 3x0, 314, '3 'j 
proof-plane, 402 
saturation, 102, 330 

„ BeetZf on, 11$ 

screen, 84 
shell, 107, 192, 31X (>^) 

„ ^ force due to, 127 

„ * potential due t^o, 127, 3:^ 
storms, X45, 309 . 
substances, 85, 339 
units, 32X 
writing, xxi 

Magnetisation, coefficient of (or sus- 
ceptibility), 89, 3x3 
intensity of, 3x3 
lamellar, 107 

mechanical effects of, 1x3 
methods of, 92-98, 327 
solenoidal, X07 
sound of, X 1 3, 434 
time needed for, 330 

Magnetism, ^6 

action of, on light, X14, 387 
caused by heat, 98 
destruction of, 99 
distribution of xq4 
of gases, 339, 387 
lamellar, X07 
laws of, 8x, 1x6, 3x0, 330 
permanent, 90, 3x3 
residual, Z02 



INDEXo 



493 



Magnetism, solenoidal, 107, 314 
temporary, 90, 102, 313 
terrestrial. 88, 135 
theories of, 91, 115, 338 
unit of, 125 
Magnetite, 76 
Magneto-electricity, 74, 391 
Magneto-electric induction, 391 

machines, 407 
Magnetographs, 146 
Magnetometer, 124 

self- registering, 146 
Magneto-optic Rotations, 387 
Magnets, artificial, 77 
compound, 95 
forms of, loi 
lamellar, 107 
laminated, 95 
methods of making, 92 98 
natural, 76, 101 
power of, 103 
Mance s method, 361 
Maps, magnetic, 139 
Mariner's Compass, 134 
Marked pole, 8a 

Afascart, £., on self -registering 
apparatus, 288 
on atmospheric electricity, 308 
Matteuccu Cottlo, on physiological 
effects, 68, 230 
on electromotive • force^ in 
muscle, 231 
Maynooth Battery (see CallatCs 

Battery) 
Maxw //, James Clerks Electro- 
magnetic theory of Ligll^ 
337. 365, 390 
on Electric Images, 250 
on protection from Lightning^ 

32, 305 
on residual charge of jar, 272 
on self-repulsidn of circuit, 334 
rule for action of current on 

magnet, 103, 317 
Theorem of equivalent Mag- 
netic shell, 192, JJ18 
Theory of Magnetism, 115 
Measurements, electrical, 355-363 

magnetic, 118, 325a 
Mechanical effects of Discharge, 284, 

^3 , . 

effects of magnetisation, 113 
,, in aielectric, 272 
Medical Applications of Electricitv, 

232, 369 
Megohm, 323 
Meidinger^s Battery, I75v 
Meridian, Magnetic, 136 
Metallo-c^omv, 43a 



Microfarad condenser, 276 
Microphone, the, 437 
Milli -ampere, 323 

Mimosa, the, electric behaviour of, 230 
Minottds Battery, 176 
Mirror Galvanometer, 203 
^loisture,' effect of, i, 8, 2op 
Molecular theory of Electric action, 6 

actions of current, 221 
Moment of Couple, 123 

of inertia, 325a 

magnetic, 123 (footnote), 325a 
Morse Telegraph instrument, 425 
Mouse-mill (see Re^/enisher) 
Mullery JohanneSy on strength of 

electromagnets, 330 
Multiplier, Schweiggen^ s, iSg 
Muscular contractions, 229, 231 
Mtcsschenbroeky Peter van, dis- 
covery of Ley den Jar, 52 

on Magnetic Figures, no 
Mutual Induction, coefficient of, 320, 

397 
Mutual Potential^ coefficient of, 320 



N 

Napoleon II.Vs Battery, 182 

Needle, magnetic, 79 
Needle "telegraph, 424 
Negative electrification, 4, 300 
Newton, Sir Isaac, observations on 
action and reaction, 83 
bis lodestone, 103 
suggests electric origin of light- 
ning, 9, 302 
suggests glass ist electric 
machines, 38 
Niaudefs Battery, 173 
Nobili, Leopoldo, on muscular con- 
tractions, 68 
on currents of animal electricity, 

231 
discovers NobilVs rings, ^2 
Non-conductors, 8 
Non-electrics, 2 
North and south, 81, 135 
North magnetic pole, Uie, 81, 135 
Null methods, 263 



Oerstedt, Hans Christian^ discovers 
magnetic action of current, 1849 
- 185, 191 
Ohm, Dr, G. S., 179 

" Ohm's Law,r i«o, 345 



494 



INDEX- 



Ohm, the, or imit of resistance, 323 

,, determination* of, 364 
One-fluid theory of electricity, 6 
Optical strain, electrostatic, 386 

„ electromagnetic, 387 
Oscillations, electric, 295 

method of (for electrostatics), 

120 {footnote), 235 
method of (for magnetic mea- 
surement), 120, 121, 122, 325a 
Osmose, electric, 222 
Other sources of electricity than fric- 
tion, 10, 57 
Ozone, 208, 298, 302 (Jbotncte) 



Page, Charles G., discovers ma;jnetic 

sounds, 113 
Parallel currents, laws of, 332 
Paramagnetic, 339^ 
" Passive" state of iron, 172 {fooinoie) 
Peltier i At^uinasei \nz elcctrcmctcr^ 
260, 307 
heating effect at junctions, 380 
theory of thunderstorms, 303 
Penetrative power of discharge, 2S4 , 
Periodicity of aurora and magnetic 

storms, 144, 145, 309 
Perry and Ayrton (see Ayrton and 

Perry) 
Pile, Voltaic, 150 
Pith-bail electroscope, 2, 3 
Phosphorescence caused by dicchargs, 

292 
Photo -voltaic property of selenium, 

589 . ' 
Photophone, 389 ^ 
Physiological actions, 226, 287 
Plane, the proof-, 29 

,, for magnetism^ 402 

Plants^ Gaston, his secondary bat- 
teries, 415^ 
on globular lightning, 304 
Plants, electricity of, 69, 230 
Plate condenser, 48, 268, 277 
electrical machine, 40 
Pliicker, Julius i on ma^ne-crystallic 

action, 343' 
Po^gendorffy J , C, his battery, 165 
Pomts, density of charge on, 35, 249 

discharge at, ^9, 42, 43, 249 
Polarity, diamagnetic, 342 

magnetic, 82, 106, 115 
Polarisation (electrolytic) in battery 
cells, 163, 414 
of Voltameter, 273, 413, 415 
lemedies for, 165 



Polarised light rotated by magnetic 
forces, 387 
relay, 428 
Poles of magnets, 78, 122 

of pyroelectric crystals, 66 
of Voltaic battery, 154 
Porrefs phenomenon, 222 
Portable electrometer, 261 
Portative force, 103 
Positive and negative electrification 

4. 300 
Potential, electric, 37, 237 

„ zero, 37»^239 
magnetic, 310, 314, 315 

„ due to current, 318 
mutual, of two circuits, 319, 
320 
Pouillety Claude S, M,, sine galvan- 
ometer, 201 
tangent galvanometer, 199 
Power, transmission of, 376 
Practical Units, 323 
Preccs, William Henty, on space 

protected from lightning, 305 
Pressure producea electrification, 65 
Priestley, Joseph, on electric expan* 

sion, 273 
Prime conductor, 39 
Printing telegraphs, 423 
Pro of -plane, 20 

„ ^ (magnetic), ^02 
Poisson on magnetism m crystals 

343 
Protoplasm, electric property of, 231 
Pyrociectricity, 66 



Quadrant electrometer (Sir IV, 
Thomson's), 262 
electroscope {Henley* s), 14 
Quadruplex telegraphy, 4.28 
*• Quantity" arrangement of cells, 
' etc., 181 -.'• ♦ 

of electricity, unit of, 17, 236 
Quetelet, E,, on atmospheric elec- 
tricity, 308 
Qtdncke, Georg, on diaphragm cur- 
* rents, 224 , 
on electric expansion. 273 
on electro - optic phenomena, 
386 



B 

Ray, electric (torpedo), 68 
Recovery, elastic, 37a 



INDEX. 



495 



Redistrit)Ution of charge, 36 
Reflecting galvanometer, 202 
Registering magnetographs and elec- 
trometers, 146, 307 
/?m, Philips invention of telephone, 

434 
Relation between currents and mag- 
nets, 184, 318, 326, 391 
between current and enerp^y, 

378 
between current and heat and 
light, 366 
Relays, 426 

Replenisher, 45, 261, 262 
Repulsion and attraction of electrified 
bodies, i, 3, 18, 20, 66, 236 
and attraction, experiments on, 

43 
and attraction of currents, 331 
and attraction of magnets, 76, 
80 
Repulsion electrometers, 260 
Residual charge of Leyden jar, 53, 272 
,, of cable, 274, 430 
„ of Voltameter, 272, 

415 
magnetism, 102 
Resinous electricity, 4 
Resistance, 27, 158, 179, 346 

absolute unit of, 363, 364 
affected by temperature, 349 
light, 389 
,, ^ sound, 436 
as a velocity, 363 
bridge or balance, 358 
coils, 359 
internal, of cell, 181, 350 

,, „ measurement 

of, 361 
laws of, 347 
measurement of, 356 
cf gases, 158, 348 
of liquids, 158, 349 
specific, 348 
Retardation of currents through 

cables, 274, 296, 430 
Retentivity (magnetic), 90, 313 
Return shock or stroke, 26, 304 
Reyfnond, Du Bois^ his galvanometer, 

231 
on animal electricity, 231 
unpolarisahle electrodes, 231 
Rheocord, 356 
Rheostat, 356 
Rheometer, \ 

Rheoscope, > su footnote to \Cji 
. Rhectrope, ) 
RUss^ Peter, on electric distribution, 
3S 



Riess^ Peter, on length of spark, 291 
electric thermometer, 7.Z%{f9ot* 
note)_ 
Ritchie* s electromotor, 375 
Ritter^ Johann Wilhebny on action 
of current on sight, 228 
his secondary pile, 415 
on subjective galvanic sounds, 

230 
on the sensitive plant {Mimosa^ 
230 
Rolling friction, 10 
Romagnosi, Dr,, discovers magnetic 

action of current, 184 
Romas^ De^ his electric kite, 302 
Ronalds^ Sir Francis^ invented a 

telegraph, 423 
Rotations, electromagnetic, 335 

Arago^Sy 401 
Rowland, Henry A ., on magnetic 
effect of electric convection, 337 
on intensity of magnetisation, 
313 
Ruhmkorff's induction coil, 398 
commutator, 399 
electromagnet, 339 



s 



St. Elmo's fire, 302 {footnote) 

Salts, electrolysis of, 417 

Sanderson, J Burdon, on electric 
sensitiveness of carnivorous plants, 
231 

Sawdust battery, 158, 176 

Schweigger's multiplier, 189 

Secondary batteries, 178, 415 

Secular variations of magnetic ele- 
ments, 141 

Seebec^s discovery of thermo-elec- 
tricity, 379 

Selenium, photo-voltaic properties of, 
389 

Self-induction of circuit, 404 

Self-recording apparatus, 146, 288, 307 

Self-repulsion of current, 334 

Sensitive plant, behaviour of, 230 

Series, union of cells in, 171 

Shadows, electric, 293 

Sheet conductor, flow of electricity 
in, 3S4 

Shell, magnetic (see Magnetic Shell) 

Shock, electric, 226 
of current, 226 

'* Short-coil " instruments, 352 

Shunt, 202, 353 

Siemens, Carl Wilkebn^.oTi heating 
effect in Leyden jar, 272 



496 



INDEX. 



Siemens t Carl Wilhelm, his dynamo- 
electric machine, 409 

hi?* loixgitudinal armature, 407 
Sight affected by current, 228 
Silurui, the, 68 
Sine galvanometer, 201 
Single touch, 92 
Single-fluid cells, 169 
Siphon-recorder, 431 
Sfnee's Battery, 165, 169 
Soap-bubble, electrified, 3 
Solenoid, 329 

magnet, 314 
Solid angles, 133 
Solidification, 6i 
Sgund of magnetisation, 113 
Sounder, the, 42^ 
Sources of electnciiy, 10, 57 
Spark, 9, 43, 281 

duration of, 296 

length of, 44, 291, 302 
Specific resistance, 348 

inductive cajQcity, 21, 49, 268, 
272 
Speed of signalling, 274, 275, 256, 430 
Sphere, distribution of charge over 

35 (4» 248, 249 
S/foUiswGode, IVillmnZf on stris, 2^4 
Ste^itrt^ Balfour^ on atmo'-pheric 
electricity, 308 

OB magnetic storms, 144 
Storms, magnetic, 145 
Standards of resistance (see ResUt- 

ance Coils) 
Sts^in, dielectric, $6 
Strength of current, 158, 179 

„ in magnetic nxea- 

sure, 195, rrj 
Strei^gth of magnet pole, 102 

of nagnetic shell, 315 
Stri^ in vacuum tubes, 292, 294 
Sturgeon, IV, , invents the electro- 
magnet, 326 
Submarine telegraphs, 429 
SulzeT^s experiment, 227 
Sjmmery on two kinds of electiifica- 

tion, 4 
Surface-density of charge, 35, 248 

limit of, 248 

of magnetism, 127, 311 
Swemifnerda7?^ s frog experiment, 229 
S^'ans electric lamp, ^^4 



Tait, Peter Gutkriei electrification 
by evaporation of sulphate of copper 
solution, 63 



Taii, Peter Guthrie, thermo-elec: 

diagram, 383 

Tar:;ent galvanometer, 199 

Taste affected by cmrent, 227 

Telegraph, electric, 423 

Bairns chemical, 218 
Morse* s instrument, 425 
needle instrument, 424 

Telegraphy, diplex, 428 
duplex, 428 
quadruplex, 428 
subraanne, 429 

Telephone, Philip Reiis^ 434 
currents of 229 
Dolbear^s^ 436 
Edison's (carbon), 436 
Graliam Bell's (articulatmg), 

435 
Varle^s (condenser), 272 
Temperature affects resistance, 183 

affected by resistance, 369 
Tension of electrostatic forces, 248 

(^footnote) 
Ter quern, A,, parrot-cage experi- 
ment, 31 
Terrestrial Magnetism, 88, 135 
Test for weak currents (chemica^), 218, 
286 . 
for weak currents (physiologi* 
cal), 229 
Testing for faults, 427 
Tetanisation produced by interrupted 

currents, 230 
Theories of Electricity, 6, 300, and 

preface, ix. 
Theories of Magnetism, 91, 115 

„ Amperes, 338 
„ I4^'Vwgll*Si IIS 
Theory of Electrolysis, Joule s^ 414 

Grotth)css*s and Clansius's, 41S 
Thermo-electric currents, ) 
Thermo-electricity, [ 70» 379 

Thermo-electric Diagp-am, 383 
Thermo-el&otromotive Series, 382 
Thermo-pile, 384 

'Thompson, Silvanus PhilUps^ on 
magnetic figures due to cur 
rents, 33^ 
on AlagTietic writing, iix 
on NobilVs rings, 422 
on Positive and Negative 
^'States, 300 

on opacity of Tourmaline, 390 
( footnote) ' 
Thomson, Joseph /., on Contact 

Electricity, 73 ; value of "x^," 365 
Thomson, Sir IVilliam, the Re- 
plenisher (or MoUse-Mill), 45, 26 1. 
263 



INDEX. 



497 



Thomson^ Sir William^ Proof of 
Contact Electricity, 71 
Attracted - disc Electrometers, 

261 
Divided-ring Electrometer, 71 
Electric convection of Heat 
(the " Thamson-^^^Qt "), 383 
Mirror Galvanometer, 202, 431 
Modified DanieiVi Battery, 176 
on atmospheric electricity, 306 
on Electric Images, 250 
on length of spark, 291 
on nomenclature of Magnet 

Poles, 81 {footnote) 
on sounds in condensers, 272 
predicts electric oscillations 

295 {^footnote) 
Quadrant Electrometer, 262 
Siphon Recorder, 431 
Thermo-electric Diagram, 383 
Wat«»r-dropping Collector, 307 
Thunder, 9, 304 
Thimderstorms, 302 

Theory of, 303 
Tinfoil Condensers, 47, 275 
Tongs, Discharging-, 51 
Torpedo (electric fish), 68, 218 
Torpedoes, fuzes for firing, 2&6, 370 
Torsion affected by magnetisation, 11 ^ 
Torsion Balance, or ) {Coulotfib^s) 
Torsion Electrometer f 15, 119 
Total action of magnet, 325a 
Tourmaline, 66, 297, 390 {Jbotftote) 
Transformers, 400 [37^ 

Transmission of P^wer by Electricity 
Tubes of force, 243, 311 
Two-fluid cells, 170 
Two-fluid theory, 6 
Two kinds of Electrification, 4, 5 
„ Magnetic poles, 81 
Tyndall^ Jokn^ on diamagnetic polar- 
ity, 342 
on magne-crystallic action, 343 



Unit Jar, 259 

Unit (Electrostatic) of Electricity, 17, 
236 

(Electrostatic) of Capacity, 247 

Magnetic Pole, 125 

of difference of potential, 242 

322, 323 

of Electromotive-force, 323^ 323 
of Resistance, 322, 323 
. of Strength of Currenti 196, 

323, 333 



Units, Fundamental and Derived. 
.2541 255 
dimensions of, 258, 32^ 
Electrical (Electrostatic), 357 
Electromagnetic. 322, 323 
Magnetic, 321 
Physical Dimensions of, 2581 

T. 324, 351 

Practical, 323 
Universal Discharger, 54 
Ure^ Dr,f on Animal Electricity, 229 



"z^," values of, 365, 390 
Vacuum, induction takes place 
through, 50, 84, 89 
partial, spark in, 9, 292 
spark wUl not pass through, 
291 
Vacuum-tubes, 292 
"Variation," the (see Declinution) 
Variation of Declination and Dip, 
secular, 141 ; annual, 143 ; diurnal, 
14? ; geographical, 136 
Varley, C Z''., his Telephone, 273 
Vegetables. Electricity of, 09 

carnivorous, sensitiveness of; 

235> 
Velocity uf Discharge, 206 

of Electricity (alleged), 296 ^ 
of Liffht, 365, 390 
Verdet^s Constant, 387 
Vibration produces Electrification, r^ 
Vitreous electricity, 4 
Volt, the, 323 

Volta^ AlessandrOy his Electrophori:-, 
22 
Condensing Electroscope, 7:, 

149 
Contact Series, 72 
Crown of Cups, 151 
on Atmospheric Electricity, 307 
on Contact Electricity, 71, 148 
on Electric Expansion, 273 
on Electrification due to com- 
bustion, 62 
Subjective Sounds due to 

Current. 228 
Volta*s Law, 72, 148, 156 
Voltaic Pile, 150 
Voltaic Electricity (see Current Elec- 
tricity) 
Arc, 371 

Battery, 154, 167; Pile, 150 
Cell, simple, 152 
Voltameter, 214, 215, 216 
Voltmeter, 360 {,d) 



49S 



INDEX. 



W 

Water, Electrolysis of, 206, 413 
Weber, the 323 

Weber ^ IVilkelnty. the Electro-dyna- 
mometer, 3;j6 
on diamagnetic polarity, 342 
Wheat stone ^ Sir Charles ^ on the 
brush discharge, 290 
Automatic Telegraph, ^23 
Dynamo -electric Machmes, 4c3 
on supposed velocity of elec- 
tricity, 296 
Wheats ton^s Bridge or Bal- 
ance, 358 
Wiedcntann^ Gustav^ on effect of 
mapmetisxn on torsion, 113 



Wiedemanfty Gnstavy en diamag* 

netism of platinum, 339 
Wilde, Henry ^ Electric Candle, 373 
Magneto-electric Machine, 40J 
Wind, Electric, 43 
WdhUf's Cell, 182 
WollastotCs Battery, 169 
Wminer on dielectric capacity, 270 



Zanr&onVs Dry Pile, 13, 182, 264 
ZanotHy experiment on grasshoppo 

229 
Zero Potential, 37, «3<) 



INDEX TO CHAPTERS XIII-XV. 



Adjustable Vacuum Tube, 460 

Alternate Currents, 476 

Alternators, 479 

Anode in Vacuum Tube, 450 

Antennae, 448 

Attuning of Waves, 442, 446 

B 

Bianodic Focus Tube, 459 

Block and Wave, 442 

Bombardment in Vacuum Tube, 45i 

Branly^s Coherer, 444 

Brush Arc-Lighting Machine, 481 

Bus Bars, 468 



Cathode in Vacuum Tube, 450 

Cathode Kays, 451 

Central Station, 466 

Choking Coil, 477 

Coherer, 444, 448 

Compound Wound Dynamo, 481 

Counter Electromotive Force, 474 

Coupled Alternators. 479 

Crookes^s Tube, 449 



Cathode Rays by a 
Dynamo and 



Deflection of 

Magnet, 453 
Difference between 

Motor. 473 
Di-phase Currents, 480 
Dislocation of Hip. 464, 465 
Distributors. 468 
Dynan-,o and Motor. 473 
Dynamos, ClnSFes of 4^1 



E 

Elasticity of Ether, 443 

Electric Egg, 449 

Ether. 442 

Ether Waves, 440, 442 

Exhaustion of Vacuum Tube, 461 

F 

Feeders, 468 

Five-Wire System, 469, 472 

Fluorescence, 450 

Focus Tube. 459 

Frequency of Alternations, 476 



Gerssler Tube, 449 



Hard and Soft Vacuum Tubes, 456 
Hertzian Waves, 441 
Hertz's Wave Detector. 441 
High Frequency Currents, 478 
High Pressure System, 470 



Impedance, 477 

Induction Coils in Wireless Teieg 

raphy,446, 447 
Induction Coil of X-Ray Apparatus, 

462 
Inertia of Ether, 443 



Kathode, see Cathode 



INDEX. 



499 



Lag and Lead, 477 
Lodge'' s Coherer, 444 
Lorenz. Dr., of Vienna, 465 
Low Pressure System, 468 
Luxations, Congenital, 465 

M 

Marconi" s Silver Coherer, 444 
MarconVs System of Wireless Teleg- 
raphy. 445 
Medium Pressure System, 469 
Motor Dynamo, 469 
Motors, Modern, 482 

N 

Numberof Vibrations of Sound, Light, 
and Electric Waves, 433 



Occlusion of Air in Metal Film, 459 
Omnibus Bars, 468 
OnestVs Coherer, 444 
Oscillatory Nature of a Leyden Jar 
Discharge, 441, 443 



Phase, 477 

Plates for Radiography, 463 
Polyphase Currents, 480 
Propelling Drag in a Motor, 474 



Radiant State, 451 

Radium, 457 

Railway Motor, 48$ 

Receiver of Wireless Message, 447 

Reflection and Refraction of Electro- 
magnetic Waves, 441 

Relay in Wireless Receiving Station, 
448 

Resistance of Vacuum Tube, 456 

Roentgen's Discovery, 454 

Rotor, 480 



Series Wound Dynamo, 481 
Shunt Wound Dynamo, 481 



Sine Wave, 476 

Slaby's System of Wireless Teleg- 
raphy, 448 
Striation in Vacuum Tube, 450 
Switchboard, 471 
Synchroniser, 479 
Synchronising of Waves, 442, 446 
Synchronous Motors, 480 



Testa's Polyphase Motor, 484 
Tesla's High Frequency, 444 
Thomson-Houston Stationary Motor, 

483 
Time of Exposure in Radiography, 464 
Toepler's Pumps, 461 
Transformation, 467 
Transmitter of Wireless Message, 446 
Transparency to X-Rays, 452 
Transverse Vibrations of Ether, 4S2 
Trembler Magnet, 448 
Tri-phase Currents, 480 
Torque, 475 
Types of Dynamos and Motors Used 

on Various Circuits, 486 



Uses of X-Rays, 465 



Vacuum Tube, 449, 450 

Velocity of Electric and Light Waves, 

441 
Vertical Wire in Marconi System, 446, 

447, 448 

W 

Wire Gauge Table, 487 



X-Ray Apparatus, 458 
X-Rays, 449 

X-Rays, Discovery of, 454 
X-Rays, Nature of, 456 
X-Rays, Properties of, 4S5 
X-Rays, Source of, 457 
X-Rays, Uses of, 465 



II 28^ ^^ 



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